KILLED
proof of input_y5SknymKPH.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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), 0 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), 2 ms]
    (12) typed CpxTrs
    (13) OrderProof [LOWER BOUND(ID), 0 ms]
    (14) typed CpxTrs
    (15) RewriteLemmaProof [LOWER BOUND(ID), 6828 ms]
    (16) typed CpxTrs
    (17) RewriteLemmaProof [LOWER BOUND(ID), 248 ms]
    (18) typed CpxTrs
    (19) RewriteLemmaProof [LOWER BOUND(ID), 1570 ms]
    (20) typed CpxTrs
    (21) RewriteLemmaProof [LOWER BOUND(ID), 1807 ms]
    (22) BEST
        (23) proven lower bound
            (24) LowerBoundPropagationProof [FINISHED, 0 ms]
            (25) BOUNDS(n^1, INF)
        (26) typed CpxTrs
(27) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(28) CpxWeightedTrs
    (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) CpxTypedWeightedTrs
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) NarrowingProof [BOTH BOUNDS(ID, ID), 608 ms]
        (34) CpxTypedWeightedCompleteTrs
        (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (36) CpxRNTS
        (37) InliningProof [UPPER BOUND(ID), 214 ms]
        (38) CpxRNTS
        (39) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CpxRNTS
    (41) CompletionProof [UPPER BOUND(ID), 0 ms]
    (42) CpxTypedWeightedCompleteTrs
        (43) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms]
        (44) CpxRNTS
(45) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(46) CdtProblem
    (47) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CpxRelTRS
        (53) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (54) CpxTRS
        (55) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (56) CpxWeightedTrs
            (57) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (58) CpxTypedWeightedTrs
            (59) CompletionProof [UPPER BOUND(ID), 0 ms]
            (60) CpxTypedWeightedCompleteTrs
            (61) CompletionProof [UPPER BOUND(ID), 0 ms]
            (62) CpxTypedWeightedCompleteTrs
                (63) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms]
                (64) CpxRNTS
    (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (66) CdtProblem
        (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CdtProblem
        (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms]
        (70) CdtProblem
        (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms]
        (76) CdtProblem
        (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms]
        (84) CdtProblem
        (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms]
        (102) CdtProblem
        (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms]
        (116) CdtProblem
        (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 34 ms]
        (122) CdtProblem
        (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms]
        (126) CdtProblem
        (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (130) CdtProblem
        (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (132) CdtProblem
        (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 12 ms]
        (134) CdtProblem
        (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (136) CdtProblem
        (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 72 ms]
        (138) CdtProblem
        (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms]
        (140) CdtProblem
        (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms]
        (142) CdtProblem
        (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 12 ms]
        (144) CdtProblem
        (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms]
        (146) CdtProblem
        (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms]
        (148) CdtProblem
        (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (150) CdtProblem
        (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms]
        (152) CdtProblem
        (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 58 ms]
        (154) CdtProblem
        (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (156) CdtProblem
        (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 62 ms]
        (158) CdtProblem
        (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (160) CdtProblem
        (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 58 ms]
        (162) CdtProblem
        (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (164) CdtProblem
        (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms]
        (166) CdtProblem
        (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (168) CdtProblem
        (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms]
        (170) CdtProblem
        (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 107 ms]
        (174) CdtProblem
        (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (176) CdtProblem
        (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 53 ms]
        (178) CdtProblem
        (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms]
        (180) CdtProblem
        (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms]
        (182) CdtProblem
        (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 16 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), 33 ms]
        (190) CdtProblem
        (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (192) CdtProblem
        (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 67 ms]
        (194) CdtProblem
        (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (196) CdtProblem
        (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms]
        (198) CdtProblem
        (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms]
        (200) CdtProblem
        (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 68 ms]
        (202) CdtProblem
        (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms]
        (204) CdtProblem
        (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 64 ms]
        (206) CdtProblem
        (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (208) CdtProblem
        (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 29 ms]
        (210) CdtProblem
        (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 18 ms]
        (212) CdtProblem
        (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms]
        (214) CdtProblem
        (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (216) CdtProblem
        (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms]
        (218) CdtProblem
        (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (220) CdtProblem
        (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms]
        (222) CdtProblem
        (223) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 13 ms]
        (224) CdtProblem
        (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (226) CdtProblem
        (227) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (228) CdtProblem
        (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms]
        (230) CdtProblem
        (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (232) CdtProblem
        (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms]
        (234) CdtProblem
        (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms]
        (236) CdtProblem
        (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 97 ms]
        (238) CdtProblem
        (239) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms]
        (240) 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, N) -> mark(N)
   a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__U31(tt) -> 0
   a__U41(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
   a__and(tt, X) -> mark(X)
   a__isNat(0) -> tt
   a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
   a__isNat(s(V1)) -> a__isNat(V1)
   a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
   a__plus(N, 0) -> a__U11(a__isNat(N), N)
   a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N)
   a__x(N, 0) -> a__U31(a__isNat(N))
   a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N)
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(U31(X)) -> a__U31(mark(X))
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(isNat(X)) -> a__isNat(X)
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(0) -> 0
   a__U11(X1, X2) -> U11(X1, X2)
   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
   a__plus(X1, X2) -> plus(X1, X2)
   a__U31(X) -> U31(X)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__x(X1, X2) -> x(X1, X2)
   a__and(X1, X2) -> and(X1, X2)
   a__isNat(X) -> isNat(X)

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

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

(2)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   a__U11(tt, N) -> mark(N)
   a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__U31(tt) -> 0'
   a__U41(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
   a__and(tt, X) -> mark(X)
   a__isNat(0') -> tt
   a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
   a__isNat(s(V1)) -> a__isNat(V1)
   a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
   a__plus(N, 0') -> a__U11(a__isNat(N), N)
   a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N)
   a__x(N, 0') -> a__U31(a__isNat(N))
   a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N)
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(U31(X)) -> a__U31(mark(X))
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(isNat(X)) -> a__isNat(X)
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(0') -> 0'
   a__U11(X1, X2) -> U11(X1, X2)
   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
   a__plus(X1, X2) -> plus(X1, X2)
   a__U31(X) -> U31(X)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__x(X1, X2) -> x(X1, X2)
   a__and(X1, X2) -> and(X1, X2)
   a__isNat(X) -> isNat(X)

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

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

(4)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   a__U11(tt, N) -> mark(N)
   a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__U31(tt) -> 0
   a__U41(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
   a__and(tt, X) -> mark(X)
   a__isNat(0) -> tt
   a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
   a__isNat(s(V1)) -> a__isNat(V1)
   a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
   a__plus(N, 0) -> a__U11(a__isNat(N), N)
   a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N)
   a__x(N, 0) -> a__U31(a__isNat(N))
   a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N)
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(U31(X)) -> a__U31(mark(X))
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(isNat(X)) -> a__isNat(X)
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(0) -> 0
   a__U11(X1, X2) -> U11(X1, X2)
   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
   a__plus(X1, X2) -> plus(X1, X2)
   a__U31(X) -> U31(X)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__x(X1, X2) -> x(X1, X2)
   a__and(X1, X2) -> and(X1, X2)
   a__isNat(X) -> isNat(X)

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) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U11(z0, z1) -> c1
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(z0, z1, z2) -> c4
   A__U31(tt) -> c5
   A__U31(z0) -> c6
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U41(z0, z1, z2) -> c10
   A__AND(tt, z0) -> c11(MARK(z0))
   A__AND(z0, z1) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(z0) -> c17
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c20
   A__X(z0, 0) -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, z1) -> c23
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(tt) -> c34
   MARK(s(z0)) -> c35(MARK(z0))
   MARK(0) -> c36
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U11(z0, z1) -> c1
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(z0, z1, z2) -> c4
   A__U31(tt) -> c5
   A__U31(z0) -> c6
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U41(z0, z1, z2) -> c10
   A__AND(tt, z0) -> c11(MARK(z0))
   A__AND(z0, z1) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(z0) -> c17
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c20
   A__X(z0, 0) -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, z1) -> c23
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(tt) -> c34
   MARK(s(z0)) -> c35(MARK(z0))
   MARK(0) -> c36
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U21_3, A__U31_1, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c1, c2_2, c3_2, c4, c5, c6, c7_3, c8_3, c9_2, c10, c11_1, c12, c13, c14_2, c15_1, c16_2, c17, c18_2, c19_3, c20, c21_2, c22_3, c23, c24_2, c25_2, c26_2, c27_2, c28_2, c29_2, c30_2, c31_2, c32_2, c33_1, c34, c35_1, c36


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

(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(MARK(z0))
   A__U11(z0, z1) -> c1
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(z0, z1, z2) -> c4
   A__U31(tt) -> c5
   A__U31(z0) -> c6
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U41(z0, z1, z2) -> c10
   A__AND(tt, z0) -> c11(MARK(z0))
   A__AND(z0, z1) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(z0) -> c17
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c20
   A__X(z0, 0) -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, z1) -> c23
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(tt) -> c34
   MARK(s(z0)) -> c35(MARK(z0))
   MARK(0) -> c36

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

   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   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(MARK(z0))
   A__U11(z0, z1) -> c1
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(z0, z1, z2) -> c4
   A__U31(tt) -> c5
   A__U31(z0) -> c6
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U41(z0, z1, z2) -> c10
   A__AND(tt, z0) -> c11(MARK(z0))
   A__AND(z0, z1) -> c12
   A__ISNAT(0') -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(z0) -> c17
   A__PLUS(z0, 0') -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c20
   A__X(z0, 0') -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, z1) -> c23
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(tt) -> c34
   MARK(s(z0)) -> c35(MARK(z0))
   MARK(0') -> c36

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

   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0'
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0') -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0') -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0') -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   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(MARK(z0))
A__U11(z0, z1) -> c1
A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U21(z0, z1, z2) -> c4
A__U31(tt) -> c5
A__U31(z0) -> c6
A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U41(z0, z1, z2) -> c10
A__AND(tt, z0) -> c11(MARK(z0))
A__AND(z0, z1) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(z0) -> c17
A__PLUS(z0, 0') -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__PLUS(z0, z1) -> c20
A__X(z0, 0') -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__X(z0, z1) -> c23
MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
MARK(isNat(z0)) -> c33(A__ISNAT(z0))
MARK(tt) -> c34
MARK(s(z0)) -> c35(MARK(z0))
MARK(0') -> c36
a__U11(tt, z0) -> mark(z0)
a__U11(z0, z1) -> U11(z0, z1)
a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U31(tt) -> 0'
a__U31(z0) -> U31(z0)
a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U11(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> a__U31(a__isNat(z0))
a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U31(z0)) -> a__U31(mark(z0))
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(and(z0, z1)) -> a__and(mark(z0), z1)
mark(isNat(z0)) -> a__isNat(z0)
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c:c1
tt :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c:c1
MARK :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c1 :: c:c1
A__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c2:c3:c4
c2 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
A__PLUS :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c18:c19:c20
mark :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c3 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
c4 :: c2:c3:c4
A__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c5:c6
c5 :: c5:c6
c6 :: c5:c6
A__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c7:c8:c9:c10
c7 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
a__x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
A__X :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c21:c22:c23
c8 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c9 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
A__AND :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c11:c12
c11 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c11:c12
c12 :: c11:c12
A__ISNAT :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c13:c14:c15:c16:c17
0' :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c13 :: c13:c14:c15:c16:c17
plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c14 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
a__isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
s :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c15 :: c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c16 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
c17 :: c13:c14:c15:c16:c17
c18 :: c:c1 -> c13:c14:c15:c16:c17 -> c18:c19:c20
c19 :: c2:c3:c4 -> c11:c12 -> c13:c14:c15:c16:c17 -> c18:c19:c20
a__and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c20 :: c18:c19:c20
c21 :: c5:c6 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c22 :: c7:c8:c9:c10 -> c11:c12 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c23 :: c21:c22:c23
U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c24 :: c:c1 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c25 :: c2:c3:c4 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c26 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c27 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c28 :: c5:c6 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c29 :: c7:c8:c9:c10 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c30 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c31 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c32 :: c11:c12 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c33 :: c13:c14:c15:c16:c17 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c34 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c35 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c36 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
a__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c:c11_37 :: c:c1
hole_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and2_37 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c363_37 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
hole_c2:c3:c44_37 :: c2:c3:c4
hole_c18:c19:c205_37 :: c18:c19:c20
hole_c5:c66_37 :: c5:c6
hole_c7:c8:c9:c107_37 :: c7:c8:c9:c10
hole_c21:c22:c238_37 :: c21:c22:c23
hole_c11:c129_37 :: c11:c12
hole_c13:c14:c15:c16:c1710_37 :: c13:c14:c15:c16:c17
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37 :: Nat -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37 :: Nat -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
gen_c13:c14:c15:c16:c1713_37 :: Nat -> c13:c14:c15:c16:c17

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

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
A__U11, MARK, A__U21, A__PLUS, mark, A__U41, a__x, A__X, A__AND, A__ISNAT, a__isNat, a__and, a__U11, a__U21, a__plus, a__U41

They will be analysed ascendingly in the following order:
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__PLUS
A__U11 = A__U41
A__U11 = A__X
A__U11 = A__AND
A__U11 = A__ISNAT
MARK = A__U21
MARK = A__PLUS
mark < MARK
MARK = A__U41
MARK = A__X
MARK = A__AND
MARK = A__ISNAT
A__U21 = A__PLUS
mark < A__U21
A__U21 = A__U41
A__U21 = A__X
A__U21 = A__AND
A__U21 = A__ISNAT
A__PLUS = A__U41
A__PLUS = A__X
A__PLUS = A__AND
A__PLUS = A__ISNAT
a__isNat < A__PLUS
a__and < A__PLUS
mark < A__U41
mark = a__x
mark = a__isNat
mark = a__and
mark = a__U11
mark = a__U21
mark = a__plus
mark = a__U41
a__x < A__U41
A__U41 = A__X
A__U41 = A__AND
A__U41 = A__ISNAT
a__x = a__isNat
a__x = a__and
a__x = a__U11
a__x = a__U21
a__x = a__plus
a__x = a__U41
A__X = A__AND
A__X = A__ISNAT
a__isNat < A__X
a__and < A__X
A__AND = A__ISNAT
a__isNat < A__ISNAT
a__isNat = a__and
a__isNat = a__U11
a__isNat = a__U21
a__isNat = a__plus
a__isNat = a__U41
a__and = a__U11
a__and = a__U21
a__and = a__plus
a__and = a__U41
a__U11 = a__U21
a__U11 = a__plus
a__U11 = a__U41
a__U21 = a__plus
a__U21 = a__U41
a__plus = a__U41

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

(14)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0) -> c(MARK(z0))
A__U11(z0, z1) -> c1
A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U21(z0, z1, z2) -> c4
A__U31(tt) -> c5
A__U31(z0) -> c6
A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U41(z0, z1, z2) -> c10
A__AND(tt, z0) -> c11(MARK(z0))
A__AND(z0, z1) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(z0) -> c17
A__PLUS(z0, 0') -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__PLUS(z0, z1) -> c20
A__X(z0, 0') -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__X(z0, z1) -> c23
MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
MARK(isNat(z0)) -> c33(A__ISNAT(z0))
MARK(tt) -> c34
MARK(s(z0)) -> c35(MARK(z0))
MARK(0') -> c36
a__U11(tt, z0) -> mark(z0)
a__U11(z0, z1) -> U11(z0, z1)
a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U31(tt) -> 0'
a__U31(z0) -> U31(z0)
a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U11(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> a__U31(a__isNat(z0))
a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U31(z0)) -> a__U31(mark(z0))
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(and(z0, z1)) -> a__and(mark(z0), z1)
mark(isNat(z0)) -> a__isNat(z0)
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c:c1
tt :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c:c1
MARK :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c1 :: c:c1
A__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c2:c3:c4
c2 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
A__PLUS :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c18:c19:c20
mark :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c3 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
c4 :: c2:c3:c4
A__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c5:c6
c5 :: c5:c6
c6 :: c5:c6
A__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c7:c8:c9:c10
c7 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
a__x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
A__X :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c21:c22:c23
c8 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c9 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
A__AND :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c11:c12
c11 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c11:c12
c12 :: c11:c12
A__ISNAT :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c13:c14:c15:c16:c17
0' :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c13 :: c13:c14:c15:c16:c17
plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c14 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
a__isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
s :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c15 :: c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c16 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
c17 :: c13:c14:c15:c16:c17
c18 :: c:c1 -> c13:c14:c15:c16:c17 -> c18:c19:c20
c19 :: c2:c3:c4 -> c11:c12 -> c13:c14:c15:c16:c17 -> c18:c19:c20
a__and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c20 :: c18:c19:c20
c21 :: c5:c6 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c22 :: c7:c8:c9:c10 -> c11:c12 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c23 :: c21:c22:c23
U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c24 :: c:c1 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c25 :: c2:c3:c4 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c26 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c27 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c28 :: c5:c6 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c29 :: c7:c8:c9:c10 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c30 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c31 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c32 :: c11:c12 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c33 :: c13:c14:c15:c16:c17 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c34 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c35 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c36 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
a__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c:c11_37 :: c:c1
hole_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and2_37 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c363_37 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
hole_c2:c3:c44_37 :: c2:c3:c4
hole_c18:c19:c205_37 :: c18:c19:c20
hole_c5:c66_37 :: c5:c6
hole_c7:c8:c9:c107_37 :: c7:c8:c9:c10
hole_c21:c22:c238_37 :: c21:c22:c23
hole_c11:c129_37 :: c11:c12
hole_c13:c14:c15:c16:c1710_37 :: c13:c14:c15:c16:c17
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37 :: Nat -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37 :: Nat -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
gen_c13:c14:c15:c16:c1713_37 :: Nat -> c13:c14:c15:c16:c17


Generator Equations:
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(0) <=> tt
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(x), tt)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(0) <=> c33(c13)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(+(x, 1)) <=> c24(c(c33(c13)), gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(x))
gen_c13:c14:c15:c16:c1713_37(0) <=> c13
gen_c13:c14:c15:c16:c1713_37(+(x, 1)) <=> c14(c11(c33(c13)), gen_c13:c14:c15:c16:c1713_37(x))


The following defined symbols remain to be analysed:
a__U11, A__U11, MARK, A__U21, A__PLUS, mark, A__U41, a__x, A__X, A__AND, A__ISNAT, a__isNat, a__and, a__U21, a__plus, a__U41

They will be analysed ascendingly in the following order:
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__PLUS
A__U11 = A__U41
A__U11 = A__X
A__U11 = A__AND
A__U11 = A__ISNAT
MARK = A__U21
MARK = A__PLUS
mark < MARK
MARK = A__U41
MARK = A__X
MARK = A__AND
MARK = A__ISNAT
A__U21 = A__PLUS
mark < A__U21
A__U21 = A__U41
A__U21 = A__X
A__U21 = A__AND
A__U21 = A__ISNAT
A__PLUS = A__U41
A__PLUS = A__X
A__PLUS = A__AND
A__PLUS = A__ISNAT
a__isNat < A__PLUS
a__and < A__PLUS
mark < A__U41
mark = a__x
mark = a__isNat
mark = a__and
mark = a__U11
mark = a__U21
mark = a__plus
mark = a__U41
a__x < A__U41
A__U41 = A__X
A__U41 = A__AND
A__U41 = A__ISNAT
a__x = a__isNat
a__x = a__and
a__x = a__U11
a__x = a__U21
a__x = a__plus
a__x = a__U41
A__X = A__AND
A__X = A__ISNAT
a__isNat < A__X
a__and < A__X
A__AND = A__ISNAT
a__isNat < A__ISNAT
a__isNat = a__and
a__isNat = a__U11
a__isNat = a__U21
a__isNat = a__plus
a__isNat = a__U41
a__and = a__U11
a__and = a__U21
a__and = a__plus
a__and = a__U41
a__U11 = a__U21
a__U11 = a__plus
a__U11 = a__U41
a__U21 = a__plus
a__U21 = a__U41
a__plus = a__U41

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

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n461713_37)) -> gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n461713_37), rt in Omega(0)

Induction Base:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(0)) ->_R^Omega(0)
tt

Induction Step:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(n461713_37, 1))) ->_R^Omega(0)
a__plus(mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n461713_37)), mark(tt)) ->_IH
a__plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(c461714_37), mark(tt)) ->_R^Omega(0)
a__plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n461713_37), tt) ->_R^Omega(0)
plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n461713_37), 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(MARK(z0))
A__U11(z0, z1) -> c1
A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U21(z0, z1, z2) -> c4
A__U31(tt) -> c5
A__U31(z0) -> c6
A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U41(z0, z1, z2) -> c10
A__AND(tt, z0) -> c11(MARK(z0))
A__AND(z0, z1) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(z0) -> c17
A__PLUS(z0, 0') -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__PLUS(z0, z1) -> c20
A__X(z0, 0') -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__X(z0, z1) -> c23
MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
MARK(isNat(z0)) -> c33(A__ISNAT(z0))
MARK(tt) -> c34
MARK(s(z0)) -> c35(MARK(z0))
MARK(0') -> c36
a__U11(tt, z0) -> mark(z0)
a__U11(z0, z1) -> U11(z0, z1)
a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U31(tt) -> 0'
a__U31(z0) -> U31(z0)
a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U11(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> a__U31(a__isNat(z0))
a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U31(z0)) -> a__U31(mark(z0))
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(and(z0, z1)) -> a__and(mark(z0), z1)
mark(isNat(z0)) -> a__isNat(z0)
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c:c1
tt :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c:c1
MARK :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c1 :: c:c1
A__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c2:c3:c4
c2 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
A__PLUS :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c18:c19:c20
mark :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c3 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
c4 :: c2:c3:c4
A__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c5:c6
c5 :: c5:c6
c6 :: c5:c6
A__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c7:c8:c9:c10
c7 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
a__x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
A__X :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c21:c22:c23
c8 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c9 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
A__AND :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c11:c12
c11 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c11:c12
c12 :: c11:c12
A__ISNAT :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c13:c14:c15:c16:c17
0' :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c13 :: c13:c14:c15:c16:c17
plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c14 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
a__isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
s :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c15 :: c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c16 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
c17 :: c13:c14:c15:c16:c17
c18 :: c:c1 -> c13:c14:c15:c16:c17 -> c18:c19:c20
c19 :: c2:c3:c4 -> c11:c12 -> c13:c14:c15:c16:c17 -> c18:c19:c20
a__and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c20 :: c18:c19:c20
c21 :: c5:c6 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c22 :: c7:c8:c9:c10 -> c11:c12 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c23 :: c21:c22:c23
U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c24 :: c:c1 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c25 :: c2:c3:c4 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c26 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c27 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c28 :: c5:c6 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c29 :: c7:c8:c9:c10 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c30 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c31 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c32 :: c11:c12 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c33 :: c13:c14:c15:c16:c17 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c34 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c35 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c36 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
a__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c:c11_37 :: c:c1
hole_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and2_37 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c363_37 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
hole_c2:c3:c44_37 :: c2:c3:c4
hole_c18:c19:c205_37 :: c18:c19:c20
hole_c5:c66_37 :: c5:c6
hole_c7:c8:c9:c107_37 :: c7:c8:c9:c10
hole_c21:c22:c238_37 :: c21:c22:c23
hole_c11:c129_37 :: c11:c12
hole_c13:c14:c15:c16:c1710_37 :: c13:c14:c15:c16:c17
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37 :: Nat -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37 :: Nat -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
gen_c13:c14:c15:c16:c1713_37 :: Nat -> c13:c14:c15:c16:c17


Lemmas:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n461713_37)) -> gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n461713_37), rt in Omega(0)


Generator Equations:
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(0) <=> tt
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(x), tt)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(0) <=> c33(c13)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(+(x, 1)) <=> c24(c(c33(c13)), gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(x))
gen_c13:c14:c15:c16:c1713_37(0) <=> c13
gen_c13:c14:c15:c16:c1713_37(+(x, 1)) <=> c14(c11(c33(c13)), gen_c13:c14:c15:c16:c1713_37(x))


The following defined symbols remain to be analysed:
a__U21, A__U11, MARK, A__U21, A__PLUS, A__U41, a__x, A__X, A__AND, A__ISNAT, a__isNat, a__and, a__U11, a__plus, a__U41

They will be analysed ascendingly in the following order:
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__PLUS
A__U11 = A__U41
A__U11 = A__X
A__U11 = A__AND
A__U11 = A__ISNAT
MARK = A__U21
MARK = A__PLUS
mark < MARK
MARK = A__U41
MARK = A__X
MARK = A__AND
MARK = A__ISNAT
A__U21 = A__PLUS
mark < A__U21
A__U21 = A__U41
A__U21 = A__X
A__U21 = A__AND
A__U21 = A__ISNAT
A__PLUS = A__U41
A__PLUS = A__X
A__PLUS = A__AND
A__PLUS = A__ISNAT
a__isNat < A__PLUS
a__and < A__PLUS
mark < A__U41
mark = a__x
mark = a__isNat
mark = a__and
mark = a__U11
mark = a__U21
mark = a__plus
mark = a__U41
a__x < A__U41
A__U41 = A__X
A__U41 = A__AND
A__U41 = A__ISNAT
a__x = a__isNat
a__x = a__and
a__x = a__U11
a__x = a__U21
a__x = a__plus
a__x = a__U41
A__X = A__AND
A__X = A__ISNAT
a__isNat < A__X
a__and < A__X
A__AND = A__ISNAT
a__isNat < A__ISNAT
a__isNat = a__and
a__isNat = a__U11
a__isNat = a__U21
a__isNat = a__plus
a__isNat = a__U41
a__and = a__U11
a__and = a__U21
a__and = a__plus
a__and = a__U41
a__U11 = a__U21
a__U11 = a__plus
a__U11 = a__U41
a__U21 = a__plus
a__U21 = a__U41
a__plus = a__U41

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

(17) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__isNat(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n614163_37))) -> *14_37, rt in Omega(0)

Induction Base:
a__isNat(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, 0)))

Induction Step:
a__isNat(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, +(n614163_37, 1)))) ->_R^Omega(0)
a__and(a__isNat(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n614163_37))), isNat(tt)) ->_IH
a__and(*14_37, isNat(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(MARK(z0))
A__U11(z0, z1) -> c1
A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U21(z0, z1, z2) -> c4
A__U31(tt) -> c5
A__U31(z0) -> c6
A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U41(z0, z1, z2) -> c10
A__AND(tt, z0) -> c11(MARK(z0))
A__AND(z0, z1) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(z0) -> c17
A__PLUS(z0, 0') -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__PLUS(z0, z1) -> c20
A__X(z0, 0') -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__X(z0, z1) -> c23
MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
MARK(isNat(z0)) -> c33(A__ISNAT(z0))
MARK(tt) -> c34
MARK(s(z0)) -> c35(MARK(z0))
MARK(0') -> c36
a__U11(tt, z0) -> mark(z0)
a__U11(z0, z1) -> U11(z0, z1)
a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U31(tt) -> 0'
a__U31(z0) -> U31(z0)
a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U11(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> a__U31(a__isNat(z0))
a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U31(z0)) -> a__U31(mark(z0))
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(and(z0, z1)) -> a__and(mark(z0), z1)
mark(isNat(z0)) -> a__isNat(z0)
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c:c1
tt :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c:c1
MARK :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c1 :: c:c1
A__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c2:c3:c4
c2 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
A__PLUS :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c18:c19:c20
mark :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c3 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
c4 :: c2:c3:c4
A__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c5:c6
c5 :: c5:c6
c6 :: c5:c6
A__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c7:c8:c9:c10
c7 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
a__x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
A__X :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c21:c22:c23
c8 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c9 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
A__AND :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c11:c12
c11 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c11:c12
c12 :: c11:c12
A__ISNAT :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c13:c14:c15:c16:c17
0' :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c13 :: c13:c14:c15:c16:c17
plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c14 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
a__isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
s :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c15 :: c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c16 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
c17 :: c13:c14:c15:c16:c17
c18 :: c:c1 -> c13:c14:c15:c16:c17 -> c18:c19:c20
c19 :: c2:c3:c4 -> c11:c12 -> c13:c14:c15:c16:c17 -> c18:c19:c20
a__and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c20 :: c18:c19:c20
c21 :: c5:c6 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c22 :: c7:c8:c9:c10 -> c11:c12 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c23 :: c21:c22:c23
U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c24 :: c:c1 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c25 :: c2:c3:c4 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c26 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c27 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c28 :: c5:c6 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c29 :: c7:c8:c9:c10 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c30 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c31 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c32 :: c11:c12 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c33 :: c13:c14:c15:c16:c17 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c34 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c35 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c36 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
a__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c:c11_37 :: c:c1
hole_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and2_37 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c363_37 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
hole_c2:c3:c44_37 :: c2:c3:c4
hole_c18:c19:c205_37 :: c18:c19:c20
hole_c5:c66_37 :: c5:c6
hole_c7:c8:c9:c107_37 :: c7:c8:c9:c10
hole_c21:c22:c238_37 :: c21:c22:c23
hole_c11:c129_37 :: c11:c12
hole_c13:c14:c15:c16:c1710_37 :: c13:c14:c15:c16:c17
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37 :: Nat -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37 :: Nat -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
gen_c13:c14:c15:c16:c1713_37 :: Nat -> c13:c14:c15:c16:c17


Lemmas:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n461713_37)) -> gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n461713_37), rt in Omega(0)
a__isNat(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n614163_37))) -> *14_37, rt in Omega(0)


Generator Equations:
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(0) <=> tt
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(x), tt)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(0) <=> c33(c13)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(+(x, 1)) <=> c24(c(c33(c13)), gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(x))
gen_c13:c14:c15:c16:c1713_37(0) <=> c13
gen_c13:c14:c15:c16:c1713_37(+(x, 1)) <=> c14(c11(c33(c13)), gen_c13:c14:c15:c16:c1713_37(x))


The following defined symbols remain to be analysed:
a__and, A__U11, MARK, A__U21, A__PLUS, mark, A__U41, a__x, A__X, A__AND, A__ISNAT, a__U11, a__U21, a__plus, a__U41

They will be analysed ascendingly in the following order:
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__PLUS
A__U11 = A__U41
A__U11 = A__X
A__U11 = A__AND
A__U11 = A__ISNAT
MARK = A__U21
MARK = A__PLUS
mark < MARK
MARK = A__U41
MARK = A__X
MARK = A__AND
MARK = A__ISNAT
A__U21 = A__PLUS
mark < A__U21
A__U21 = A__U41
A__U21 = A__X
A__U21 = A__AND
A__U21 = A__ISNAT
A__PLUS = A__U41
A__PLUS = A__X
A__PLUS = A__AND
A__PLUS = A__ISNAT
a__isNat < A__PLUS
a__and < A__PLUS
mark < A__U41
mark = a__x
mark = a__isNat
mark = a__and
mark = a__U11
mark = a__U21
mark = a__plus
mark = a__U41
a__x < A__U41
A__U41 = A__X
A__U41 = A__AND
A__U41 = A__ISNAT
a__x = a__isNat
a__x = a__and
a__x = a__U11
a__x = a__U21
a__x = a__plus
a__x = a__U41
A__X = A__AND
A__X = A__ISNAT
a__isNat < A__X
a__and < A__X
A__AND = A__ISNAT
a__isNat < A__ISNAT
a__isNat = a__and
a__isNat = a__U11
a__isNat = a__U21
a__isNat = a__plus
a__isNat = a__U41
a__and = a__U11
a__and = a__U21
a__and = a__plus
a__and = a__U41
a__U11 = a__U21
a__U11 = a__plus
a__U11 = a__U41
a__U21 = a__plus
a__U21 = a__U41
a__plus = a__U41

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

(19) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37)) -> gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37), rt in Omega(0)

Induction Base:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(0)) ->_R^Omega(0)
tt

Induction Step:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(n618301_37, 1))) ->_R^Omega(0)
a__plus(mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37)), mark(tt)) ->_IH
a__plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(c618302_37), mark(tt)) ->_R^Omega(0)
a__plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37), tt) ->_R^Omega(0)
plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37), tt)

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

(20)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0) -> c(MARK(z0))
A__U11(z0, z1) -> c1
A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U21(z0, z1, z2) -> c4
A__U31(tt) -> c5
A__U31(z0) -> c6
A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U41(z0, z1, z2) -> c10
A__AND(tt, z0) -> c11(MARK(z0))
A__AND(z0, z1) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(z0) -> c17
A__PLUS(z0, 0') -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__PLUS(z0, z1) -> c20
A__X(z0, 0') -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__X(z0, z1) -> c23
MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
MARK(isNat(z0)) -> c33(A__ISNAT(z0))
MARK(tt) -> c34
MARK(s(z0)) -> c35(MARK(z0))
MARK(0') -> c36
a__U11(tt, z0) -> mark(z0)
a__U11(z0, z1) -> U11(z0, z1)
a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U31(tt) -> 0'
a__U31(z0) -> U31(z0)
a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U11(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> a__U31(a__isNat(z0))
a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U31(z0)) -> a__U31(mark(z0))
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(and(z0, z1)) -> a__and(mark(z0), z1)
mark(isNat(z0)) -> a__isNat(z0)
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c:c1
tt :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c:c1
MARK :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c1 :: c:c1
A__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c2:c3:c4
c2 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
A__PLUS :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c18:c19:c20
mark :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c3 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
c4 :: c2:c3:c4
A__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c5:c6
c5 :: c5:c6
c6 :: c5:c6
A__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c7:c8:c9:c10
c7 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
a__x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
A__X :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c21:c22:c23
c8 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c9 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
A__AND :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c11:c12
c11 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c11:c12
c12 :: c11:c12
A__ISNAT :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c13:c14:c15:c16:c17
0' :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c13 :: c13:c14:c15:c16:c17
plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c14 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
a__isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
s :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c15 :: c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c16 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
c17 :: c13:c14:c15:c16:c17
c18 :: c:c1 -> c13:c14:c15:c16:c17 -> c18:c19:c20
c19 :: c2:c3:c4 -> c11:c12 -> c13:c14:c15:c16:c17 -> c18:c19:c20
a__and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c20 :: c18:c19:c20
c21 :: c5:c6 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c22 :: c7:c8:c9:c10 -> c11:c12 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c23 :: c21:c22:c23
U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c24 :: c:c1 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c25 :: c2:c3:c4 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c26 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c27 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c28 :: c5:c6 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c29 :: c7:c8:c9:c10 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c30 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c31 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c32 :: c11:c12 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c33 :: c13:c14:c15:c16:c17 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c34 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c35 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c36 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
a__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c:c11_37 :: c:c1
hole_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and2_37 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c363_37 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
hole_c2:c3:c44_37 :: c2:c3:c4
hole_c18:c19:c205_37 :: c18:c19:c20
hole_c5:c66_37 :: c5:c6
hole_c7:c8:c9:c107_37 :: c7:c8:c9:c10
hole_c21:c22:c238_37 :: c21:c22:c23
hole_c11:c129_37 :: c11:c12
hole_c13:c14:c15:c16:c1710_37 :: c13:c14:c15:c16:c17
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37 :: Nat -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37 :: Nat -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
gen_c13:c14:c15:c16:c1713_37 :: Nat -> c13:c14:c15:c16:c17


Lemmas:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37)) -> gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37), rt in Omega(0)
a__isNat(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n614163_37))) -> *14_37, rt in Omega(0)


Generator Equations:
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(0) <=> tt
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(x), tt)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(0) <=> c33(c13)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(+(x, 1)) <=> c24(c(c33(c13)), gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(x))
gen_c13:c14:c15:c16:c1713_37(0) <=> c13
gen_c13:c14:c15:c16:c1713_37(+(x, 1)) <=> c14(c11(c33(c13)), gen_c13:c14:c15:c16:c1713_37(x))


The following defined symbols remain to be analysed:
a__U21, A__U11, MARK, A__U21, A__PLUS, A__U41, A__X, A__AND, A__ISNAT, a__plus

They will be analysed ascendingly in the following order:
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__PLUS
A__U11 = A__U41
A__U11 = A__X
A__U11 = A__AND
A__U11 = A__ISNAT
MARK = A__U21
MARK = A__PLUS
mark < MARK
MARK = A__U41
MARK = A__X
MARK = A__AND
MARK = A__ISNAT
A__U21 = A__PLUS
mark < A__U21
A__U21 = A__U41
A__U21 = A__X
A__U21 = A__AND
A__U21 = A__ISNAT
A__PLUS = A__U41
A__PLUS = A__X
A__PLUS = A__AND
A__PLUS = A__ISNAT
a__isNat < A__PLUS
a__and < A__PLUS
mark < A__U41
mark = a__x
mark = a__isNat
mark = a__and
mark = a__U11
mark = a__U21
mark = a__plus
mark = a__U41
a__x < A__U41
A__U41 = A__X
A__U41 = A__AND
A__U41 = A__ISNAT
a__x = a__isNat
a__x = a__and
a__x = a__U11
a__x = a__U21
a__x = a__plus
a__x = a__U41
A__X = A__AND
A__X = A__ISNAT
a__isNat < A__X
a__and < A__X
A__AND = A__ISNAT
a__isNat < A__ISNAT
a__isNat = a__and
a__isNat = a__U11
a__isNat = a__U21
a__isNat = a__plus
a__isNat = a__U41
a__and = a__U11
a__and = a__U21
a__and = a__plus
a__and = a__U41
a__U11 = a__U21
a__U11 = a__plus
a__U11 = a__U41
a__U21 = a__plus
a__U21 = a__U41
a__plus = a__U41

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

(21) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MARK(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n771061_37))) -> *14_37, rt in Omega(n771061_37)

Induction Base:
MARK(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, 0)))

Induction Step:
MARK(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, +(n771061_37, 1)))) ->_R^Omega(1)
c26(A__PLUS(mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n771061_37))), mark(tt)), MARK(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n771061_37)))) ->_L^Omega(0)
c26(A__PLUS(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n771061_37)), mark(tt)), MARK(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n771061_37)))) ->_L^Omega(0)
c26(A__PLUS(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n771061_37)), gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(0)), MARK(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n771061_37)))) ->_R^Omega(1)
c26(c20, MARK(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n771061_37)))) ->_IH
c26(c20, *14_37)

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

(22)
Complex Obligation (BEST)

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

(23)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
A__U11(tt, z0) -> c(MARK(z0))
A__U11(z0, z1) -> c1
A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U21(z0, z1, z2) -> c4
A__U31(tt) -> c5
A__U31(z0) -> c6
A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U41(z0, z1, z2) -> c10
A__AND(tt, z0) -> c11(MARK(z0))
A__AND(z0, z1) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(z0) -> c17
A__PLUS(z0, 0') -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__PLUS(z0, z1) -> c20
A__X(z0, 0') -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__X(z0, z1) -> c23
MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
MARK(isNat(z0)) -> c33(A__ISNAT(z0))
MARK(tt) -> c34
MARK(s(z0)) -> c35(MARK(z0))
MARK(0') -> c36
a__U11(tt, z0) -> mark(z0)
a__U11(z0, z1) -> U11(z0, z1)
a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U31(tt) -> 0'
a__U31(z0) -> U31(z0)
a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U11(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> a__U31(a__isNat(z0))
a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U31(z0)) -> a__U31(mark(z0))
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(and(z0, z1)) -> a__and(mark(z0), z1)
mark(isNat(z0)) -> a__isNat(z0)
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c:c1
tt :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c:c1
MARK :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c1 :: c:c1
A__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c2:c3:c4
c2 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
A__PLUS :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c18:c19:c20
mark :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c3 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
c4 :: c2:c3:c4
A__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c5:c6
c5 :: c5:c6
c6 :: c5:c6
A__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c7:c8:c9:c10
c7 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
a__x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
A__X :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c21:c22:c23
c8 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c9 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
A__AND :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c11:c12
c11 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c11:c12
c12 :: c11:c12
A__ISNAT :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c13:c14:c15:c16:c17
0' :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c13 :: c13:c14:c15:c16:c17
plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c14 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
a__isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
s :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c15 :: c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c16 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
c17 :: c13:c14:c15:c16:c17
c18 :: c:c1 -> c13:c14:c15:c16:c17 -> c18:c19:c20
c19 :: c2:c3:c4 -> c11:c12 -> c13:c14:c15:c16:c17 -> c18:c19:c20
a__and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c20 :: c18:c19:c20
c21 :: c5:c6 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c22 :: c7:c8:c9:c10 -> c11:c12 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c23 :: c21:c22:c23
U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c24 :: c:c1 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c25 :: c2:c3:c4 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c26 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c27 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c28 :: c5:c6 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c29 :: c7:c8:c9:c10 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c30 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c31 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c32 :: c11:c12 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c33 :: c13:c14:c15:c16:c17 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c34 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c35 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c36 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
a__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c:c11_37 :: c:c1
hole_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and2_37 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c363_37 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
hole_c2:c3:c44_37 :: c2:c3:c4
hole_c18:c19:c205_37 :: c18:c19:c20
hole_c5:c66_37 :: c5:c6
hole_c7:c8:c9:c107_37 :: c7:c8:c9:c10
hole_c21:c22:c238_37 :: c21:c22:c23
hole_c11:c129_37 :: c11:c12
hole_c13:c14:c15:c16:c1710_37 :: c13:c14:c15:c16:c17
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37 :: Nat -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37 :: Nat -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
gen_c13:c14:c15:c16:c1713_37 :: Nat -> c13:c14:c15:c16:c17


Lemmas:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37)) -> gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37), rt in Omega(0)
a__isNat(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n614163_37))) -> *14_37, rt in Omega(0)


Generator Equations:
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(0) <=> tt
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(x), tt)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(0) <=> c33(c13)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(+(x, 1)) <=> c24(c(c33(c13)), gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(x))
gen_c13:c14:c15:c16:c1713_37(0) <=> c13
gen_c13:c14:c15:c16:c1713_37(+(x, 1)) <=> c14(c11(c33(c13)), gen_c13:c14:c15:c16:c1713_37(x))


The following defined symbols remain to be analysed:
MARK, A__U11, A__U21, A__PLUS, A__U41, A__X, A__AND, A__ISNAT

They will be analysed ascendingly in the following order:
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__PLUS
A__U11 = A__U41
A__U11 = A__X
A__U11 = A__AND
A__U11 = A__ISNAT
MARK = A__U21
MARK = A__PLUS
MARK = A__U41
MARK = A__X
MARK = A__AND
MARK = A__ISNAT
A__U21 = A__PLUS
A__U21 = A__U41
A__U21 = A__X
A__U21 = A__AND
A__U21 = A__ISNAT
A__PLUS = A__U41
A__PLUS = A__X
A__PLUS = A__AND
A__PLUS = A__ISNAT
A__U41 = A__X
A__U41 = A__AND
A__U41 = A__ISNAT
A__X = A__AND
A__X = A__ISNAT
A__AND = A__ISNAT

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

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

(25)
BOUNDS(n^1, INF)

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

(26)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0) -> c(MARK(z0))
A__U11(z0, z1) -> c1
A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U21(z0, z1, z2) -> c4
A__U31(tt) -> c5
A__U31(z0) -> c6
A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U41(z0, z1, z2) -> c10
A__AND(tt, z0) -> c11(MARK(z0))
A__AND(z0, z1) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
A__ISNAT(z0) -> c17
A__PLUS(z0, 0') -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__PLUS(z0, z1) -> c20
A__X(z0, 0') -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
A__X(z0, z1) -> c23
MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
MARK(isNat(z0)) -> c33(A__ISNAT(z0))
MARK(tt) -> c34
MARK(s(z0)) -> c35(MARK(z0))
MARK(0') -> c36
a__U11(tt, z0) -> mark(z0)
a__U11(z0, z1) -> U11(z0, z1)
a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U31(tt) -> 0'
a__U31(z0) -> U31(z0)
a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U11(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> a__U31(a__isNat(z0))
a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U31(z0)) -> a__U31(mark(z0))
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(and(z0, z1)) -> a__and(mark(z0), z1)
mark(isNat(z0)) -> a__isNat(z0)
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c:c1
tt :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c:c1
MARK :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c1 :: c:c1
A__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c2:c3:c4
c2 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
A__PLUS :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c18:c19:c20
mark :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c3 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c2:c3:c4
c4 :: c2:c3:c4
A__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c5:c6
c5 :: c5:c6
c6 :: c5:c6
A__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c7:c8:c9:c10
c7 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
a__x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
A__X :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c21:c22:c23
c8 :: c18:c19:c20 -> c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c9 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
A__AND :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c11:c12
c11 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c11:c12
c12 :: c11:c12
A__ISNAT :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> c13:c14:c15:c16:c17
0' :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c13 :: c13:c14:c15:c16:c17
plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c14 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
a__isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
isNat :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
s :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c15 :: c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
x :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c16 :: c11:c12 -> c13:c14:c15:c16:c17 -> c13:c14:c15:c16:c17
c17 :: c13:c14:c15:c16:c17
c18 :: c:c1 -> c13:c14:c15:c16:c17 -> c18:c19:c20
c19 :: c2:c3:c4 -> c11:c12 -> c13:c14:c15:c16:c17 -> c18:c19:c20
a__and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c20 :: c18:c19:c20
c21 :: c5:c6 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c22 :: c7:c8:c9:c10 -> c11:c12 -> c13:c14:c15:c16:c17 -> c21:c22:c23
c23 :: c21:c22:c23
U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c24 :: c:c1 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c25 :: c2:c3:c4 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c26 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c27 :: c18:c19:c20 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c28 :: c5:c6 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c29 :: c7:c8:c9:c10 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c30 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c31 :: c21:c22:c23 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
and :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
c32 :: c11:c12 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c33 :: c13:c14:c15:c16:c17 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c34 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c35 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
c36 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
a__U11 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U21 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__plus :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U31 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
a__U41 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c:c11_37 :: c:c1
hole_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and2_37 :: tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
hole_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c363_37 :: c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
hole_c2:c3:c44_37 :: c2:c3:c4
hole_c18:c19:c205_37 :: c18:c19:c20
hole_c5:c66_37 :: c5:c6
hole_c7:c8:c9:c107_37 :: c7:c8:c9:c10
hole_c21:c22:c238_37 :: c21:c22:c23
hole_c11:c129_37 :: c11:c12
hole_c13:c14:c15:c16:c1710_37 :: c13:c14:c15:c16:c17
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37 :: Nat -> tt:0':plus:isNat:s:x:U11:U21:U31:U41:and
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37 :: Nat -> c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36
gen_c13:c14:c15:c16:c1713_37 :: Nat -> c13:c14:c15:c16:c17


Lemmas:
mark(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37)) -> gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(n618301_37), rt in Omega(0)
a__isNat(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n614163_37))) -> *14_37, rt in Omega(0)
MARK(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(1, n771061_37))) -> *14_37, rt in Omega(n771061_37)


Generator Equations:
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(0) <=> tt
gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:x:U11:U21:U31:U41:and11_37(x), tt)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(0) <=> c33(c13)
gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(+(x, 1)) <=> c24(c(c33(c13)), gen_c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c3612_37(x))
gen_c13:c14:c15:c16:c1713_37(0) <=> c13
gen_c13:c14:c15:c16:c1713_37(+(x, 1)) <=> c14(c11(c33(c13)), gen_c13:c14:c15:c16:c1713_37(x))


The following defined symbols remain to be analysed:
A__U11, A__U21, A__PLUS, A__U41, A__X, A__AND, A__ISNAT

They will be analysed ascendingly in the following order:
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__PLUS
A__U11 = A__U41
A__U11 = A__X
A__U11 = A__AND
A__U11 = A__ISNAT
MARK = A__U21
MARK = A__PLUS
MARK = A__U41
MARK = A__X
MARK = A__AND
MARK = A__ISNAT
A__U21 = A__PLUS
A__U21 = A__U41
A__U21 = A__X
A__U21 = A__AND
A__U21 = A__ISNAT
A__PLUS = A__U41
A__PLUS = A__X
A__PLUS = A__AND
A__PLUS = A__ISNAT
A__U41 = A__X
A__U41 = A__AND
A__U41 = A__ISNAT
A__X = A__AND
A__X = A__ISNAT
A__AND = A__ISNAT

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

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

(28)
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, N) -> mark(N) [1]
   a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U31(tt) -> 0 [1]
   a__U41(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) [1]
   a__isNat(s(V1)) -> a__isNat(V1) [1]
   a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) [1]
   a__plus(N, 0) -> a__U11(a__isNat(N), N) [1]
   a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) [1]
   a__x(N, 0) -> a__U31(a__isNat(N)) [1]
   a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N) [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U31(X)) -> a__U31(mark(X)) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNat(X)) -> a__isNat(X) [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__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U31(X) -> U31(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]

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

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

(30)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   a__U11(tt, N) -> mark(N) [1]
   a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U31(tt) -> 0 [1]
   a__U41(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) [1]
   a__isNat(s(V1)) -> a__isNat(V1) [1]
   a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) [1]
   a__plus(N, 0) -> a__U11(a__isNat(N), N) [1]
   a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) [1]
   a__x(N, 0) -> a__U31(a__isNat(N)) [1]
   a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N) [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U31(X)) -> a__U31(mark(X)) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNat(X)) -> a__isNat(X) [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__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U31(X) -> U31(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
tt :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
mark :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U21 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
s :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__plus :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U31 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
0 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U41 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__x :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__and :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__isNat :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
plus :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
isNat :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
x :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U11 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U21 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U31 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U41 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
and :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and

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

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

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

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:
none

(c) The following functions are completely defined:

   mark_1
   a__and_2
   a__isNat_1
   a__x_2
   a__U21_3
   a__U41_3
   a__plus_2
   a__U11_2
   a__U31_1

Due to the following rules being added:
none

And the following fresh constants: none

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

(32)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   a__U11(tt, N) -> mark(N) [1]
   a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U31(tt) -> 0 [1]
   a__U41(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) [1]
   a__isNat(s(V1)) -> a__isNat(V1) [1]
   a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) [1]
   a__plus(N, 0) -> a__U11(a__isNat(N), N) [1]
   a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) [1]
   a__x(N, 0) -> a__U31(a__isNat(N)) [1]
   a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N) [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U31(X)) -> a__U31(mark(X)) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNat(X)) -> a__isNat(X) [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__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U31(X) -> U31(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
tt :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
mark :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U21 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
s :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__plus :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U31 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
0 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U41 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__x :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__and :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__isNat :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
plus :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
isNat :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
x :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U11 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U21 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U31 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U41 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
and :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and

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

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

(34)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   a__U11(tt, N) -> mark(N) [1]
   a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U31(tt) -> 0 [1]
   a__U41(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(0, V2)) -> a__and(tt, isNat(V2)) [2]
   a__isNat(plus(plus(V1', V2'), V2)) -> a__and(a__and(a__isNat(V1'), isNat(V2')), isNat(V2)) [2]
   a__isNat(plus(s(V1''), V2)) -> a__and(a__isNat(V1''), isNat(V2)) [2]
   a__isNat(plus(x(V11, V2''), V2)) -> a__and(a__and(a__isNat(V11), isNat(V2'')), isNat(V2)) [2]
   a__isNat(plus(V1, V2)) -> a__and(isNat(V1), isNat(V2)) [2]
   a__isNat(s(V1)) -> a__isNat(V1) [1]
   a__isNat(x(0, V2)) -> a__and(tt, isNat(V2)) [2]
   a__isNat(x(plus(V12, V21), V2)) -> a__and(a__and(a__isNat(V12), isNat(V21)), isNat(V2)) [2]
   a__isNat(x(s(V13), V2)) -> a__and(a__isNat(V13), isNat(V2)) [2]
   a__isNat(x(x(V14, V22), V2)) -> a__and(a__and(a__isNat(V14), isNat(V22)), isNat(V2)) [2]
   a__isNat(x(V1, V2)) -> a__and(isNat(V1), isNat(V2)) [2]
   a__plus(0, 0) -> a__U11(tt, 0) [2]
   a__plus(plus(V15, V23), 0) -> a__U11(a__and(a__isNat(V15), isNat(V23)), plus(V15, V23)) [2]
   a__plus(s(V16), 0) -> a__U11(a__isNat(V16), s(V16)) [2]
   a__plus(x(V17, V24), 0) -> a__U11(a__and(a__isNat(V17), isNat(V24)), x(V17, V24)) [2]
   a__plus(N, 0) -> a__U11(isNat(N), N) [2]
   a__plus(N, s(0)) -> a__U21(a__and(tt, isNat(N)), 0, N) [2]
   a__plus(N, s(plus(V18, V25))) -> a__U21(a__and(a__and(a__isNat(V18), isNat(V25)), isNat(N)), plus(V18, V25), N) [2]
   a__plus(N, s(s(V19))) -> a__U21(a__and(a__isNat(V19), isNat(N)), s(V19), N) [2]
   a__plus(N, s(x(V110, V26))) -> a__U21(a__and(a__and(a__isNat(V110), isNat(V26)), isNat(N)), x(V110, V26), N) [2]
   a__plus(N, s(M)) -> a__U21(a__and(isNat(M), isNat(N)), M, N) [2]
   a__x(0, 0) -> a__U31(tt) [2]
   a__x(plus(V111, V27), 0) -> a__U31(a__and(a__isNat(V111), isNat(V27))) [2]
   a__x(s(V112), 0) -> a__U31(a__isNat(V112)) [2]
   a__x(x(V113, V28), 0) -> a__U31(a__and(a__isNat(V113), isNat(V28))) [2]
   a__x(N, 0) -> a__U31(isNat(N)) [2]
   a__x(N, s(0)) -> a__U41(a__and(tt, isNat(N)), 0, N) [2]
   a__x(N, s(plus(V114, V29))) -> a__U41(a__and(a__and(a__isNat(V114), isNat(V29)), isNat(N)), plus(V114, V29), N) [2]
   a__x(N, s(s(V115))) -> a__U41(a__and(a__isNat(V115), isNat(N)), s(V115), N) [2]
   a__x(N, s(x(V116, V210))) -> a__U41(a__and(a__and(a__isNat(V116), isNat(V210)), isNat(N)), x(V116, V210), N) [2]
   a__x(N, s(M)) -> a__U41(a__and(isNat(M), isNat(N)), M, N) [2]
   mark(U11(U11(X1143, X2143), X2)) -> a__U11(a__U11(mark(X1143), X2143), X2) [2]
   mark(U11(U21(X1144, X2144, X349), X2)) -> a__U11(a__U21(mark(X1144), X2144, X349), X2) [2]
   mark(U11(plus(X1145, X2145), X2)) -> a__U11(a__plus(mark(X1145), mark(X2145)), X2) [2]
   mark(U11(U31(X99), X2)) -> a__U11(a__U31(mark(X99)), X2) [2]
   mark(U11(U41(X1146, X2146, X350), X2)) -> a__U11(a__U41(mark(X1146), X2146, X350), X2) [2]
   mark(U11(x(X1147, X2147), X2)) -> a__U11(a__x(mark(X1147), mark(X2147)), X2) [2]
   mark(U11(and(X1148, X2148), X2)) -> a__U11(a__and(mark(X1148), X2148), X2) [2]
   mark(U11(isNat(X100), X2)) -> a__U11(a__isNat(X100), X2) [2]
   mark(U11(tt, X2)) -> a__U11(tt, X2) [2]
   mark(U11(s(X101), X2)) -> a__U11(s(mark(X101)), X2) [2]
   mark(U11(0, X2)) -> a__U11(0, X2) [2]
   mark(U21(U11(X1149, X2149), X2, X3)) -> a__U21(a__U11(mark(X1149), X2149), X2, X3) [2]
   mark(U21(U21(X1150, X2150, X351), X2, X3)) -> a__U21(a__U21(mark(X1150), X2150, X351), X2, X3) [2]
   mark(U21(plus(X1151, X2151), X2, X3)) -> a__U21(a__plus(mark(X1151), mark(X2151)), X2, X3) [2]
   mark(U21(U31(X102), X2, X3)) -> a__U21(a__U31(mark(X102)), X2, X3) [2]
   mark(U21(U41(X1152, X2152, X352), X2, X3)) -> a__U21(a__U41(mark(X1152), X2152, X352), X2, X3) [2]
   mark(U21(x(X1153, X2153), X2, X3)) -> a__U21(a__x(mark(X1153), mark(X2153)), X2, X3) [2]
   mark(U21(and(X1154, X2154), X2, X3)) -> a__U21(a__and(mark(X1154), X2154), X2, X3) [2]
   mark(U21(isNat(X103), X2, X3)) -> a__U21(a__isNat(X103), X2, X3) [2]
   mark(U21(tt, X2, X3)) -> a__U21(tt, X2, X3) [2]
   mark(U21(s(X104), X2, X3)) -> a__U21(s(mark(X104)), X2, X3) [2]
   mark(U21(0, X2, X3)) -> a__U21(0, X2, X3) [2]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U31(U11(X1227, X2227))) -> a__U31(a__U11(mark(X1227), X2227)) [2]
   mark(U31(U21(X1228, X2228, X388))) -> a__U31(a__U21(mark(X1228), X2228, X388)) [2]
   mark(U31(plus(X1229, X2229))) -> a__U31(a__plus(mark(X1229), mark(X2229))) [2]
   mark(U31(U31(X389))) -> a__U31(a__U31(mark(X389))) [2]
   mark(U31(U41(X1230, X2230, X390))) -> a__U31(a__U41(mark(X1230), X2230, X390)) [2]
   mark(U31(x(X1231, X2231))) -> a__U31(a__x(mark(X1231), mark(X2231))) [2]
   mark(U31(and(X1232, X2232))) -> a__U31(a__and(mark(X1232), X2232)) [2]
   mark(U31(isNat(X391))) -> a__U31(a__isNat(X391)) [2]
   mark(U31(tt)) -> a__U31(tt) [2]
   mark(U31(s(X392))) -> a__U31(s(mark(X392))) [2]
   mark(U31(0)) -> a__U31(0) [2]
   mark(U41(U11(X1233, X2233), X2, X3)) -> a__U41(a__U11(mark(X1233), X2233), X2, X3) [2]
   mark(U41(U21(X1234, X2234, X393), X2, X3)) -> a__U41(a__U21(mark(X1234), X2234, X393), X2, X3) [2]
   mark(U41(plus(X1235, X2235), X2, X3)) -> a__U41(a__plus(mark(X1235), mark(X2235)), X2, X3) [2]
   mark(U41(U31(X394), X2, X3)) -> a__U41(a__U31(mark(X394)), X2, X3) [2]
   mark(U41(U41(X1236, X2236, X395), X2, X3)) -> a__U41(a__U41(mark(X1236), X2236, X395), X2, X3) [2]
   mark(U41(x(X1237, X2237), X2, X3)) -> a__U41(a__x(mark(X1237), mark(X2237)), X2, X3) [2]
   mark(U41(and(X1238, X2238), X2, X3)) -> a__U41(a__and(mark(X1238), X2238), X2, X3) [2]
   mark(U41(isNat(X396), X2, X3)) -> a__U41(a__isNat(X396), X2, X3) [2]
   mark(U41(tt, X2, X3)) -> a__U41(tt, X2, X3) [2]
   mark(U41(s(X397), X2, X3)) -> a__U41(s(mark(X397)), X2, X3) [2]
   mark(U41(0, X2, X3)) -> a__U41(0, X2, X3) [2]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1]
   mark(and(U11(X1311, X2311), X2)) -> a__and(a__U11(mark(X1311), X2311), X2) [2]
   mark(and(U21(X1312, X2312, X3123), X2)) -> a__and(a__U21(mark(X1312), X2312, X3123), X2) [2]
   mark(and(plus(X1313, X2313), X2)) -> a__and(a__plus(mark(X1313), mark(X2313)), X2) [2]
   mark(and(U31(X435), X2)) -> a__and(a__U31(mark(X435)), X2) [2]
   mark(and(U41(X1314, X2314, X3124), X2)) -> a__and(a__U41(mark(X1314), X2314, X3124), X2) [2]
   mark(and(x(X1315, X2315), X2)) -> a__and(a__x(mark(X1315), mark(X2315)), X2) [2]
   mark(and(and(X1316, X2316), X2)) -> a__and(a__and(mark(X1316), X2316), X2) [2]
   mark(and(isNat(X436), X2)) -> a__and(a__isNat(X436), X2) [2]
   mark(and(tt, X2)) -> a__and(tt, X2) [2]
   mark(and(s(X437), X2)) -> a__and(s(mark(X437)), X2) [2]
   mark(and(0, X2)) -> a__and(0, X2) [2]
   mark(isNat(X)) -> a__isNat(X) [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__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U31(X) -> U31(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
tt :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
mark :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U21 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
s :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__plus :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U31 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
0 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U41 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__x :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__and :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__isNat :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
plus :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
isNat :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
x :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U11 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U21 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U31 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U41 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
and :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and

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

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

   tt => 1
   0 => 0

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

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

   a__U11(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0
   a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U21(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U21(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U31(z) -{ 1 }-> 0 :|: z = 1
   a__U31(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U41(z, z', z'') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(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__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, X >= 0
   a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__isNat(z) -{ 1 }-> a__isNat(V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 2 }-> a__and(a__isNat(V1''), 1 + V2) :|: V1'' >= 0, z = 1 + (1 + V1'') + V2, V2 >= 0
   a__isNat(z) -{ 2 }-> a__and(a__isNat(V13), 1 + V2) :|: V13 >= 0, V2 >= 0, z = 1 + (1 + V13) + V2
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V1'), 1 + V2'), 1 + V2) :|: z = 1 + (1 + V1' + V2') + V2, V2 >= 0, V2' >= 0, V1' >= 0
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V11), 1 + V2''), 1 + V2) :|: V11 >= 0, V2'' >= 0, V2 >= 0, z = 1 + (1 + V11 + V2'') + V2
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V12), 1 + V21), 1 + V2) :|: V21 >= 0, z = 1 + (1 + V12 + V21) + V2, V12 >= 0, V2 >= 0
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V14), 1 + V22), 1 + V2) :|: V14 >= 0, z = 1 + (1 + V14 + V22) + V2, V22 >= 0, V2 >= 0
   a__isNat(z) -{ 2 }-> a__and(1, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNat(z) -{ 2 }-> a__and(1 + V1, 1 + 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__U21(a__and(a__isNat(V19), 1 + N), 1 + V19, N) :|: z' = 1 + (1 + V19), V19 >= 0, z = N, N >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(a__and(a__isNat(V110), 1 + V26), 1 + N), 1 + V110 + V26, N) :|: V110 >= 0, z = N, z' = 1 + (1 + V110 + V26), N >= 0, V26 >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(a__and(a__isNat(V18), 1 + V25), 1 + N), 1 + V18 + V25, N) :|: V25 >= 0, V18 >= 0, z' = 1 + (1 + V18 + V25), z = N, N >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(1, 1 + N), 0, N) :|: z = N, z' = 1 + 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(1 + M, 1 + N), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U11(a__isNat(V16), 1 + V16) :|: V16 >= 0, z = 1 + V16, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(a__and(a__isNat(V15), 1 + V23), 1 + V15 + V23) :|: z = 1 + V15 + V23, V23 >= 0, V15 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(a__and(a__isNat(V17), 1 + V24), 1 + V17 + V24) :|: V24 >= 0, z = 1 + V17 + V24, V17 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(1, 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(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
   a__x(z, z') -{ 2 }-> a__U41(a__and(a__isNat(V115), 1 + N), 1 + V115, N) :|: z' = 1 + (1 + V115), z = N, V115 >= 0, N >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(a__and(a__isNat(V114), 1 + V29), 1 + N), 1 + V114 + V29, N) :|: V114 >= 0, V29 >= 0, z = N, z' = 1 + (1 + V114 + V29), N >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(a__and(a__isNat(V116), 1 + V210), 1 + N), 1 + V116 + V210, N) :|: z' = 1 + (1 + V116 + V210), z = N, V116 >= 0, V210 >= 0, N >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(1, 1 + N), 0, N) :|: z = N, z' = 1 + 0, N >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(1 + M, 1 + N), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__x(z, z') -{ 2 }-> a__U31(a__isNat(V112)) :|: z = 1 + V112, V112 >= 0, z' = 0
   a__x(z, z') -{ 2 }-> a__U31(a__and(a__isNat(V111), 1 + V27)) :|: z = 1 + V111 + V27, V111 >= 0, V27 >= 0, z' = 0
   a__x(z, z') -{ 2 }-> a__U31(a__and(a__isNat(V113), 1 + V28)) :|: z = 1 + V113 + V28, V28 >= 0, z' = 0, V113 >= 0
   a__x(z, z') -{ 2 }-> a__U31(1) :|: z = 0, z' = 0
   a__x(z, z') -{ 2 }-> a__U31(1 + N) :|: z = N, z' = 0, N >= 0
   a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + 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__and(a__x(mark(X1315), mark(X2315)), X2) :|: X2315 >= 0, z = 1 + (1 + X1315 + X2315) + X2, X1315 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__plus(mark(X1313), mark(X2313)), X2) :|: X1313 >= 0, z = 1 + (1 + X1313 + X2313) + X2, X2 >= 0, X2313 >= 0
   mark(z) -{ 2 }-> a__and(a__isNat(X436), X2) :|: z = 1 + (1 + X436) + X2, X2 >= 0, X436 >= 0
   mark(z) -{ 2 }-> a__and(a__and(mark(X1316), X2316), X2) :|: X1316 >= 0, z = 1 + (1 + X1316 + X2316) + X2, X2316 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U41(mark(X1314), X2314, X3124), X2) :|: z = 1 + (1 + X1314 + X2314 + X3124) + X2, X2314 >= 0, X1314 >= 0, X3124 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U31(mark(X435)), X2) :|: z = 1 + (1 + X435) + X2, X2 >= 0, X435 >= 0
   mark(z) -{ 2 }-> a__and(a__U21(mark(X1312), X2312, X3123), X2) :|: X1312 >= 0, X3123 >= 0, z = 1 + (1 + X1312 + X2312 + X3123) + X2, X2 >= 0, X2312 >= 0
   mark(z) -{ 2 }-> a__and(a__U11(mark(X1311), X2311), X2) :|: X2311 >= 0, z = 1 + (1 + X1311 + X2311) + X2, X1311 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(1 + mark(X437), X2) :|: z = 1 + (1 + X437) + X2, X437 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__x(mark(X1237), mark(X2237)), X2, X3) :|: X2237 >= 0, X3 >= 0, X1237 >= 0, z = 1 + (1 + X1237 + X2237) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__plus(mark(X1235), mark(X2235)), X2, X3) :|: X1235 >= 0, X3 >= 0, X2235 >= 0, X2 >= 0, z = 1 + (1 + X1235 + X2235) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__isNat(X396), X2, X3) :|: z = 1 + (1 + X396) + X2 + X3, X3 >= 0, X2 >= 0, X396 >= 0
   mark(z) -{ 2 }-> a__U41(a__and(mark(X1238), X2238), X2, X3) :|: z = 1 + (1 + X1238 + X2238) + X2 + X3, X2238 >= 0, X3 >= 0, X2 >= 0, X1238 >= 0
   mark(z) -{ 2 }-> a__U41(a__U41(mark(X1236), X2236, X395), X2, X3) :|: X395 >= 0, X2236 >= 0, X1236 >= 0, X3 >= 0, z = 1 + (1 + X1236 + X2236 + X395) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U31(mark(X394)), X2, X3) :|: X3 >= 0, X394 >= 0, X2 >= 0, z = 1 + (1 + X394) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__U21(mark(X1234), X2234, X393), X2, X3) :|: z = 1 + (1 + X1234 + X2234 + X393) + X2 + X3, X1234 >= 0, X3 >= 0, X393 >= 0, X2 >= 0, X2234 >= 0
   mark(z) -{ 2 }-> a__U41(a__U11(mark(X1233), X2233), X2, X3) :|: X2233 >= 0, X3 >= 0, z = 1 + (1 + X1233 + X2233) + X2 + X3, X1233 >= 0, X2 >= 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(X397), X2, X3) :|: z = 1 + (1 + X397) + X2 + X3, X3 >= 0, X397 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__x(mark(X1231), mark(X2231))) :|: z = 1 + (1 + X1231 + X2231), X2231 >= 0, X1231 >= 0
   mark(z) -{ 2 }-> a__U31(a__plus(mark(X1229), mark(X2229))) :|: X2229 >= 0, X1229 >= 0, z = 1 + (1 + X1229 + X2229)
   mark(z) -{ 2 }-> a__U31(a__isNat(X391)) :|: X391 >= 0, z = 1 + (1 + X391)
   mark(z) -{ 2 }-> a__U31(a__and(mark(X1232), X2232)) :|: X2232 >= 0, X1232 >= 0, z = 1 + (1 + X1232 + X2232)
   mark(z) -{ 2 }-> a__U31(a__U41(mark(X1230), X2230, X390)) :|: z = 1 + (1 + X1230 + X2230 + X390), X2230 >= 0, X390 >= 0, X1230 >= 0
   mark(z) -{ 2 }-> a__U31(a__U31(mark(X389))) :|: X389 >= 0, z = 1 + (1 + X389)
   mark(z) -{ 2 }-> a__U31(a__U21(mark(X1228), X2228, X388)) :|: z = 1 + (1 + X1228 + X2228 + X388), X1228 >= 0, X388 >= 0, X2228 >= 0
   mark(z) -{ 2 }-> a__U31(a__U11(mark(X1227), X2227)) :|: X2227 >= 0, z = 1 + (1 + X1227 + X2227), X1227 >= 0
   mark(z) -{ 2 }-> a__U31(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__U31(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__U31(1 + mark(X392)) :|: X392 >= 0, z = 1 + (1 + X392)
   mark(z) -{ 2 }-> a__U21(a__x(mark(X1153), mark(X2153)), X2, X3) :|: X1153 >= 0, z = 1 + (1 + X1153 + X2153) + X2 + X3, X3 >= 0, X2153 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNat(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__and(mark(X1154), X2154), X2, X3) :|: z = 1 + (1 + X1154 + X2154) + X2 + X3, X3 >= 0, X1154 >= 0, X2 >= 0, X2154 >= 0
   mark(z) -{ 2 }-> a__U21(a__U41(mark(X1152), X2152, X352), X2, X3) :|: z = 1 + (1 + X1152 + X2152 + X352) + X2 + X3, X2152 >= 0, X352 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0
   mark(z) -{ 2 }-> a__U21(a__U31(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X1150), X2150, X351), X2, X3) :|: z = 1 + (1 + X1150 + X2150 + X351) + X2 + X3, X2150 >= 0, X3 >= 0, X351 >= 0, X1150 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0
   mark(z) -{ 2 }-> a__U21(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__x(mark(X1147), mark(X2147)), X2) :|: X1147 >= 0, z = 1 + (1 + X1147 + X2147) + X2, X2147 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X1145), mark(X2145)), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2) :|: z = 1 + (1 + X100) + X2, X2 >= 0, X100 >= 0
   mark(z) -{ 2 }-> a__U11(a__and(mark(X1148), X2148), X2) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2, X1148 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U41(mark(X1146), X2146, X350), X2) :|: X350 >= 0, X1146 >= 0, X2146 >= 0, X2 >= 0, z = 1 + (1 + X1146 + X2146 + X350) + X2
   mark(z) -{ 2 }-> a__U11(a__U31(mark(X99)), X2) :|: X99 >= 0, z = 1 + (1 + X99) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X1144), X2144, X349), X2) :|: X2144 >= 0, X349 >= 0, X1144 >= 0, X2 >= 0, z = 1 + (1 + X1144 + X2144 + X349) + X2
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X1143), X2143), X2) :|: z = 1 + (1 + X1143 + X2143) + X2, X2143 >= 0, X2 >= 0, X1143 >= 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(X101), X2) :|: z = 1 + (1 + X101) + X2, X2 >= 0, X101 >= 0
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0


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

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

   a__U31(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z) -{ 1 }-> 0 :|: z = 1

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

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

   a__U11(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0
   a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U21(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U21(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U31(z) -{ 1 }-> 0 :|: z = 1
   a__U31(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U41(z, z', z'') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(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__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, X >= 0
   a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__isNat(z) -{ 1 }-> a__isNat(V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 2 }-> a__and(a__isNat(V1''), 1 + V2) :|: V1'' >= 0, z = 1 + (1 + V1'') + V2, V2 >= 0
   a__isNat(z) -{ 2 }-> a__and(a__isNat(V13), 1 + V2) :|: V13 >= 0, V2 >= 0, z = 1 + (1 + V13) + V2
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V1'), 1 + V2'), 1 + V2) :|: z = 1 + (1 + V1' + V2') + V2, V2 >= 0, V2' >= 0, V1' >= 0
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V11), 1 + V2''), 1 + V2) :|: V11 >= 0, V2'' >= 0, V2 >= 0, z = 1 + (1 + V11 + V2'') + V2
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V12), 1 + V21), 1 + V2) :|: V21 >= 0, z = 1 + (1 + V12 + V21) + V2, V12 >= 0, V2 >= 0
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V14), 1 + V22), 1 + V2) :|: V14 >= 0, z = 1 + (1 + V14 + V22) + V2, V22 >= 0, V2 >= 0
   a__isNat(z) -{ 2 }-> a__and(1, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNat(z) -{ 2 }-> a__and(1 + V1, 1 + 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__U21(a__and(a__isNat(V19), 1 + N), 1 + V19, N) :|: z' = 1 + (1 + V19), V19 >= 0, z = N, N >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(a__and(a__isNat(V110), 1 + V26), 1 + N), 1 + V110 + V26, N) :|: V110 >= 0, z = N, z' = 1 + (1 + V110 + V26), N >= 0, V26 >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(a__and(a__isNat(V18), 1 + V25), 1 + N), 1 + V18 + V25, N) :|: V25 >= 0, V18 >= 0, z' = 1 + (1 + V18 + V25), z = N, N >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(1, 1 + N), 0, N) :|: z = N, z' = 1 + 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(1 + M, 1 + N), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U11(a__isNat(V16), 1 + V16) :|: V16 >= 0, z = 1 + V16, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(a__and(a__isNat(V15), 1 + V23), 1 + V15 + V23) :|: z = 1 + V15 + V23, V23 >= 0, V15 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(a__and(a__isNat(V17), 1 + V24), 1 + V17 + V24) :|: V24 >= 0, z = 1 + V17 + V24, V17 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(1, 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(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
   a__x(z, z') -{ 2 }-> a__U41(a__and(a__isNat(V115), 1 + N), 1 + V115, N) :|: z' = 1 + (1 + V115), z = N, V115 >= 0, N >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(a__and(a__isNat(V114), 1 + V29), 1 + N), 1 + V114 + V29, N) :|: V114 >= 0, V29 >= 0, z = N, z' = 1 + (1 + V114 + V29), N >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(a__and(a__isNat(V116), 1 + V210), 1 + N), 1 + V116 + V210, N) :|: z' = 1 + (1 + V116 + V210), z = N, V116 >= 0, V210 >= 0, N >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(1, 1 + N), 0, N) :|: z = N, z' = 1 + 0, N >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(1 + M, 1 + N), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__x(z, z') -{ 2 }-> a__U31(a__isNat(V112)) :|: z = 1 + V112, V112 >= 0, z' = 0
   a__x(z, z') -{ 2 }-> a__U31(a__and(a__isNat(V111), 1 + V27)) :|: z = 1 + V111 + V27, V111 >= 0, V27 >= 0, z' = 0
   a__x(z, z') -{ 2 }-> a__U31(a__and(a__isNat(V113), 1 + V28)) :|: z = 1 + V113 + V28, V28 >= 0, z' = 0, V113 >= 0
   a__x(z, z') -{ 3 }-> 0 :|: z = 0, z' = 0, 1 = 1
   a__x(z, z') -{ 3 }-> 0 :|: z = N, z' = 0, N >= 0, 1 + N = 1
   a__x(z, z') -{ 3 }-> 1 + X :|: z = 0, z' = 0, X >= 0, 1 = X
   a__x(z, z') -{ 3 }-> 1 + X :|: z = N, z' = 0, N >= 0, X >= 0, 1 + N = X
   a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + 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__and(a__x(mark(X1315), mark(X2315)), X2) :|: X2315 >= 0, z = 1 + (1 + X1315 + X2315) + X2, X1315 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__plus(mark(X1313), mark(X2313)), X2) :|: X1313 >= 0, z = 1 + (1 + X1313 + X2313) + X2, X2 >= 0, X2313 >= 0
   mark(z) -{ 2 }-> a__and(a__isNat(X436), X2) :|: z = 1 + (1 + X436) + X2, X2 >= 0, X436 >= 0
   mark(z) -{ 2 }-> a__and(a__and(mark(X1316), X2316), X2) :|: X1316 >= 0, z = 1 + (1 + X1316 + X2316) + X2, X2316 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U41(mark(X1314), X2314, X3124), X2) :|: z = 1 + (1 + X1314 + X2314 + X3124) + X2, X2314 >= 0, X1314 >= 0, X3124 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U31(mark(X435)), X2) :|: z = 1 + (1 + X435) + X2, X2 >= 0, X435 >= 0
   mark(z) -{ 2 }-> a__and(a__U21(mark(X1312), X2312, X3123), X2) :|: X1312 >= 0, X3123 >= 0, z = 1 + (1 + X1312 + X2312 + X3123) + X2, X2 >= 0, X2312 >= 0
   mark(z) -{ 2 }-> a__and(a__U11(mark(X1311), X2311), X2) :|: X2311 >= 0, z = 1 + (1 + X1311 + X2311) + X2, X1311 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__and(1 + mark(X437), X2) :|: z = 1 + (1 + X437) + X2, X437 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__x(mark(X1237), mark(X2237)), X2, X3) :|: X2237 >= 0, X3 >= 0, X1237 >= 0, z = 1 + (1 + X1237 + X2237) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__plus(mark(X1235), mark(X2235)), X2, X3) :|: X1235 >= 0, X3 >= 0, X2235 >= 0, X2 >= 0, z = 1 + (1 + X1235 + X2235) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__isNat(X396), X2, X3) :|: z = 1 + (1 + X396) + X2 + X3, X3 >= 0, X2 >= 0, X396 >= 0
   mark(z) -{ 2 }-> a__U41(a__and(mark(X1238), X2238), X2, X3) :|: z = 1 + (1 + X1238 + X2238) + X2 + X3, X2238 >= 0, X3 >= 0, X2 >= 0, X1238 >= 0
   mark(z) -{ 2 }-> a__U41(a__U41(mark(X1236), X2236, X395), X2, X3) :|: X395 >= 0, X2236 >= 0, X1236 >= 0, X3 >= 0, z = 1 + (1 + X1236 + X2236 + X395) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U31(mark(X394)), X2, X3) :|: X3 >= 0, X394 >= 0, X2 >= 0, z = 1 + (1 + X394) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__U21(mark(X1234), X2234, X393), X2, X3) :|: z = 1 + (1 + X1234 + X2234 + X393) + X2 + X3, X1234 >= 0, X3 >= 0, X393 >= 0, X2 >= 0, X2234 >= 0
   mark(z) -{ 2 }-> a__U41(a__U11(mark(X1233), X2233), X2, X3) :|: X2233 >= 0, X3 >= 0, z = 1 + (1 + X1233 + X2233) + X2 + X3, X1233 >= 0, X2 >= 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(X397), X2, X3) :|: z = 1 + (1 + X397) + X2 + X3, X3 >= 0, X397 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__x(mark(X1231), mark(X2231))) :|: z = 1 + (1 + X1231 + X2231), X2231 >= 0, X1231 >= 0
   mark(z) -{ 2 }-> a__U31(a__plus(mark(X1229), mark(X2229))) :|: X2229 >= 0, X1229 >= 0, z = 1 + (1 + X1229 + X2229)
   mark(z) -{ 2 }-> a__U31(a__isNat(X391)) :|: X391 >= 0, z = 1 + (1 + X391)
   mark(z) -{ 2 }-> a__U31(a__and(mark(X1232), X2232)) :|: X2232 >= 0, X1232 >= 0, z = 1 + (1 + X1232 + X2232)
   mark(z) -{ 2 }-> a__U31(a__U41(mark(X1230), X2230, X390)) :|: z = 1 + (1 + X1230 + X2230 + X390), X2230 >= 0, X390 >= 0, X1230 >= 0
   mark(z) -{ 2 }-> a__U31(a__U31(mark(X389))) :|: X389 >= 0, z = 1 + (1 + X389)
   mark(z) -{ 2 }-> a__U31(a__U21(mark(X1228), X2228, X388)) :|: z = 1 + (1 + X1228 + X2228 + X388), X1228 >= 0, X388 >= 0, X2228 >= 0
   mark(z) -{ 2 }-> a__U31(a__U11(mark(X1227), X2227)) :|: X2227 >= 0, z = 1 + (1 + X1227 + X2227), X1227 >= 0
   mark(z) -{ 2 }-> a__U31(1 + mark(X392)) :|: X392 >= 0, z = 1 + (1 + X392)
   mark(z) -{ 2 }-> a__U21(a__x(mark(X1153), mark(X2153)), X2, X3) :|: X1153 >= 0, z = 1 + (1 + X1153 + X2153) + X2 + X3, X3 >= 0, X2153 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNat(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__and(mark(X1154), X2154), X2, X3) :|: z = 1 + (1 + X1154 + X2154) + X2 + X3, X3 >= 0, X1154 >= 0, X2 >= 0, X2154 >= 0
   mark(z) -{ 2 }-> a__U21(a__U41(mark(X1152), X2152, X352), X2, X3) :|: z = 1 + (1 + X1152 + X2152 + X352) + X2 + X3, X2152 >= 0, X352 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0
   mark(z) -{ 2 }-> a__U21(a__U31(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X1150), X2150, X351), X2, X3) :|: z = 1 + (1 + X1150 + X2150 + X351) + X2 + X3, X2150 >= 0, X3 >= 0, X351 >= 0, X1150 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0
   mark(z) -{ 2 }-> a__U21(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__x(mark(X1147), mark(X2147)), X2) :|: X1147 >= 0, z = 1 + (1 + X1147 + X2147) + X2, X2147 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X1145), mark(X2145)), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2) :|: z = 1 + (1 + X100) + X2, X2 >= 0, X100 >= 0
   mark(z) -{ 2 }-> a__U11(a__and(mark(X1148), X2148), X2) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2, X1148 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U41(mark(X1146), X2146, X350), X2) :|: X350 >= 0, X1146 >= 0, X2146 >= 0, X2 >= 0, z = 1 + (1 + X1146 + X2146 + X350) + X2
   mark(z) -{ 2 }-> a__U11(a__U31(mark(X99)), X2) :|: X99 >= 0, z = 1 + (1 + X99) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X1144), X2144, X349), X2) :|: X2144 >= 0, X349 >= 0, X1144 >= 0, X2 >= 0, z = 1 + (1 + X1144 + X2144 + X349) + X2
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X1143), X2143), X2) :|: z = 1 + (1 + X1143 + X2143) + X2, X2143 >= 0, X2 >= 0, X1143 >= 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(X101), X2) :|: z = 1 + (1 + X101) + X2, X2 >= 0, X101 >= 0
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 0 :|: z = 1 + 1, 1 = 1
   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


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

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

   a__U11(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0
   a__U11(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U21(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0
   a__U21(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__U31(z) -{ 1 }-> 0 :|: z = 1
   a__U31(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U41(z, z', z'') -{ 1 }-> a__plus(a__x(mark(z''), mark(z')), mark(z'')) :|: z = 1, z' >= 0, z'' >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__and(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0
   a__and(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__isNat(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 2 }-> a__and(a__isNat(V1''), 1 + V2) :|: V1'' >= 0, z = 1 + (1 + V1'') + V2, V2 >= 0
   a__isNat(z) -{ 2 }-> a__and(a__isNat(V13), 1 + V2) :|: V13 >= 0, V2 >= 0, z = 1 + (1 + V13) + V2
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V1'), 1 + V2'), 1 + V2) :|: z = 1 + (1 + V1' + V2') + V2, V2 >= 0, V2' >= 0, V1' >= 0
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V11), 1 + V2''), 1 + V2) :|: V11 >= 0, V2'' >= 0, V2 >= 0, z = 1 + (1 + V11 + V2'') + V2
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V12), 1 + V21), 1 + V2) :|: V21 >= 0, z = 1 + (1 + V12 + V21) + V2, V12 >= 0, V2 >= 0
   a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V14), 1 + V22), 1 + V2) :|: V14 >= 0, z = 1 + (1 + V14 + V22) + V2, V22 >= 0, V2 >= 0
   a__isNat(z) -{ 2 }-> a__and(1, 1 + (z - 1)) :|: z - 1 >= 0
   a__isNat(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNat(z) -{ 1 }-> 1 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(a__isNat(z' - 2), 1 + z), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(a__and(a__isNat(V110), 1 + V26), 1 + z), 1 + V110 + V26, z) :|: V110 >= 0, z' = 1 + (1 + V110 + V26), z >= 0, V26 >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(a__and(a__isNat(V18), 1 + V25), 1 + z), 1 + V18 + V25, z) :|: V25 >= 0, V18 >= 0, z' = 1 + (1 + V18 + V25), z >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(1, 1 + z), 0, z) :|: z' = 1 + 0, z >= 0
   a__plus(z, z') -{ 2 }-> a__U21(a__and(1 + (z' - 1), 1 + z), z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__plus(z, z') -{ 2 }-> a__U11(a__isNat(z - 1), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(a__and(a__isNat(V15), 1 + V23), 1 + V15 + V23) :|: z = 1 + V15 + V23, V23 >= 0, V15 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(a__and(a__isNat(V17), 1 + V24), 1 + V17 + V24) :|: V24 >= 0, z = 1 + V17 + V24, V17 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(1, 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U11(1 + z, z) :|: z' = 0, z >= 0
   a__plus(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(a__isNat(z' - 2), 1 + z), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(a__and(a__isNat(V114), 1 + V29), 1 + z), 1 + V114 + V29, z) :|: V114 >= 0, V29 >= 0, z' = 1 + (1 + V114 + V29), z >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(a__and(a__isNat(V116), 1 + V210), 1 + z), 1 + V116 + V210, z) :|: z' = 1 + (1 + V116 + V210), V116 >= 0, V210 >= 0, z >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(1, 1 + z), 0, z) :|: z' = 1 + 0, z >= 0
   a__x(z, z') -{ 2 }-> a__U41(a__and(1 + (z' - 1), 1 + z), z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__x(z, z') -{ 2 }-> a__U31(a__isNat(z - 1)) :|: z - 1 >= 0, z' = 0
   a__x(z, z') -{ 2 }-> a__U31(a__and(a__isNat(V111), 1 + V27)) :|: z = 1 + V111 + V27, V111 >= 0, V27 >= 0, z' = 0
   a__x(z, z') -{ 2 }-> a__U31(a__and(a__isNat(V113), 1 + V28)) :|: z = 1 + V113 + V28, V28 >= 0, z' = 0, V113 >= 0
   a__x(z, z') -{ 3 }-> 0 :|: z = 0, z' = 0, 1 = 1
   a__x(z, z') -{ 3 }-> 0 :|: z' = 0, z >= 0, 1 + z = 1
   a__x(z, z') -{ 3 }-> 1 + X :|: z = 0, z' = 0, X >= 0, 1 = X
   a__x(z, z') -{ 3 }-> 1 + X :|: z' = 0, z >= 0, X >= 0, 1 + z = X
   a__x(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   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__and(a__x(mark(X1315), mark(X2315)), X2) :|: X2315 >= 0, z = 1 + (1 + X1315 + X2315) + X2, X1315 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__plus(mark(X1313), mark(X2313)), X2) :|: X1313 >= 0, z = 1 + (1 + X1313 + X2313) + X2, X2 >= 0, X2313 >= 0
   mark(z) -{ 2 }-> a__and(a__isNat(X436), X2) :|: z = 1 + (1 + X436) + X2, X2 >= 0, X436 >= 0
   mark(z) -{ 2 }-> a__and(a__and(mark(X1316), X2316), X2) :|: X1316 >= 0, z = 1 + (1 + X1316 + X2316) + X2, X2316 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U41(mark(X1314), X2314, X3124), X2) :|: z = 1 + (1 + X1314 + X2314 + X3124) + X2, X2314 >= 0, X1314 >= 0, X3124 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(a__U31(mark(X435)), X2) :|: z = 1 + (1 + X435) + X2, X2 >= 0, X435 >= 0
   mark(z) -{ 2 }-> a__and(a__U21(mark(X1312), X2312, X3123), X2) :|: X1312 >= 0, X3123 >= 0, z = 1 + (1 + X1312 + X2312 + X3123) + X2, X2 >= 0, X2312 >= 0
   mark(z) -{ 2 }-> a__and(a__U11(mark(X1311), X2311), X2) :|: X2311 >= 0, z = 1 + (1 + X1311 + X2311) + X2, X1311 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__and(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__and(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__and(1 + mark(X437), X2) :|: z = 1 + (1 + X437) + X2, X437 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__x(mark(X1237), mark(X2237)), X2, X3) :|: X2237 >= 0, X3 >= 0, X1237 >= 0, z = 1 + (1 + X1237 + X2237) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__plus(mark(X1235), mark(X2235)), X2, X3) :|: X1235 >= 0, X3 >= 0, X2235 >= 0, X2 >= 0, z = 1 + (1 + X1235 + X2235) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__isNat(X396), X2, X3) :|: z = 1 + (1 + X396) + X2 + X3, X3 >= 0, X2 >= 0, X396 >= 0
   mark(z) -{ 2 }-> a__U41(a__and(mark(X1238), X2238), X2, X3) :|: z = 1 + (1 + X1238 + X2238) + X2 + X3, X2238 >= 0, X3 >= 0, X2 >= 0, X1238 >= 0
   mark(z) -{ 2 }-> a__U41(a__U41(mark(X1236), X2236, X395), X2, X3) :|: X395 >= 0, X2236 >= 0, X1236 >= 0, X3 >= 0, z = 1 + (1 + X1236 + X2236 + X395) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U31(mark(X394)), X2, X3) :|: X3 >= 0, X394 >= 0, X2 >= 0, z = 1 + (1 + X394) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__U21(mark(X1234), X2234, X393), X2, X3) :|: z = 1 + (1 + X1234 + X2234 + X393) + X2 + X3, X1234 >= 0, X3 >= 0, X393 >= 0, X2 >= 0, X2234 >= 0
   mark(z) -{ 2 }-> a__U41(a__U11(mark(X1233), X2233), X2, X3) :|: X2233 >= 0, X3 >= 0, z = 1 + (1 + X1233 + X2233) + X2 + X3, X1233 >= 0, X2 >= 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(X397), X2, X3) :|: z = 1 + (1 + X397) + X2 + X3, X3 >= 0, X397 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__x(mark(X1231), mark(X2231))) :|: z = 1 + (1 + X1231 + X2231), X2231 >= 0, X1231 >= 0
   mark(z) -{ 2 }-> a__U31(a__plus(mark(X1229), mark(X2229))) :|: X2229 >= 0, X1229 >= 0, z = 1 + (1 + X1229 + X2229)
   mark(z) -{ 2 }-> a__U31(a__isNat(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U31(a__and(mark(X1232), X2232)) :|: X2232 >= 0, X1232 >= 0, z = 1 + (1 + X1232 + X2232)
   mark(z) -{ 2 }-> a__U31(a__U41(mark(X1230), X2230, X390)) :|: z = 1 + (1 + X1230 + X2230 + X390), X2230 >= 0, X390 >= 0, X1230 >= 0
   mark(z) -{ 2 }-> a__U31(a__U31(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U21(mark(X1228), X2228, X388)) :|: z = 1 + (1 + X1228 + X2228 + X388), X1228 >= 0, X388 >= 0, X2228 >= 0
   mark(z) -{ 2 }-> a__U31(a__U11(mark(X1227), X2227)) :|: X2227 >= 0, z = 1 + (1 + X1227 + X2227), X1227 >= 0
   mark(z) -{ 2 }-> a__U31(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U21(a__x(mark(X1153), mark(X2153)), X2, X3) :|: X1153 >= 0, z = 1 + (1 + X1153 + X2153) + X2 + X3, X3 >= 0, X2153 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X1151), mark(X2151)), X2, X3) :|: X2151 >= 0, X3 >= 0, X1151 >= 0, z = 1 + (1 + X1151 + X2151) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNat(X103), X2, X3) :|: X103 >= 0, z = 1 + (1 + X103) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__and(mark(X1154), X2154), X2, X3) :|: z = 1 + (1 + X1154 + X2154) + X2 + X3, X3 >= 0, X1154 >= 0, X2 >= 0, X2154 >= 0
   mark(z) -{ 2 }-> a__U21(a__U41(mark(X1152), X2152, X352), X2, X3) :|: z = 1 + (1 + X1152 + X2152 + X352) + X2 + X3, X2152 >= 0, X352 >= 0, X3 >= 0, X2 >= 0, X1152 >= 0
   mark(z) -{ 2 }-> a__U21(a__U31(mark(X102)), X2, X3) :|: z = 1 + (1 + X102) + X2 + X3, X3 >= 0, X2 >= 0, X102 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X1150), X2150, X351), X2, X3) :|: z = 1 + (1 + X1150 + X2150 + X351) + X2 + X3, X2150 >= 0, X3 >= 0, X351 >= 0, X1150 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X1149), X2149), X2, X3) :|: z = 1 + (1 + X1149 + X2149) + X2 + X3, X2149 >= 0, X3 >= 0, X2 >= 0, X1149 >= 0
   mark(z) -{ 2 }-> a__U21(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(1 + mark(X104), X2, X3) :|: X104 >= 0, X3 >= 0, z = 1 + (1 + X104) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__x(mark(X1147), mark(X2147)), X2) :|: X1147 >= 0, z = 1 + (1 + X1147 + X2147) + X2, X2147 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X1145), mark(X2145)), X2) :|: z = 1 + (1 + X1145 + X2145) + X2, X1145 >= 0, X2 >= 0, X2145 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNat(X100), X2) :|: z = 1 + (1 + X100) + X2, X2 >= 0, X100 >= 0
   mark(z) -{ 2 }-> a__U11(a__and(mark(X1148), X2148), X2) :|: X2148 >= 0, z = 1 + (1 + X1148 + X2148) + X2, X1148 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U41(mark(X1146), X2146, X350), X2) :|: X350 >= 0, X1146 >= 0, X2146 >= 0, X2 >= 0, z = 1 + (1 + X1146 + X2146 + X350) + X2
   mark(z) -{ 2 }-> a__U11(a__U31(mark(X99)), X2) :|: X99 >= 0, z = 1 + (1 + X99) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X1144), X2144, X349), X2) :|: X2144 >= 0, X349 >= 0, X1144 >= 0, X2 >= 0, z = 1 + (1 + X1144 + X2144 + X349) + X2
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X1143), X2143), X2) :|: z = 1 + (1 + X1143 + X2143) + X2, X2143 >= 0, X2 >= 0, X1143 >= 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(X101), X2) :|: z = 1 + (1 + X101) + X2, X2 >= 0, X101 >= 0
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 0 :|: z = 1 + 1, 1 = 1
   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


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

(41) 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

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

(42)
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, N) -> mark(N) [1]
   a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U31(tt) -> 0 [1]
   a__U41(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) [1]
   a__isNat(s(V1)) -> a__isNat(V1) [1]
   a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) [1]
   a__plus(N, 0) -> a__U11(a__isNat(N), N) [1]
   a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) [1]
   a__x(N, 0) -> a__U31(a__isNat(N)) [1]
   a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N) [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U31(X)) -> a__U31(mark(X)) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNat(X)) -> a__isNat(X) [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__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U31(X) -> U31(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNat(X) -> isNat(X) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
tt :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
mark :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U21 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
s :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__plus :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U31 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
0 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__U41 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__x :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__and :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
a__isNat :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
plus :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
isNat :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
x :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U11 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U21 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U31 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
U41 :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and
and :: tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and -> tt:s:0:plus:isNat:x:U11:U21:U31:U41:and

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

(43) 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

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

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0
   a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U21(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U21(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U31(z) -{ 1 }-> 0 :|: z = 1
   a__U31(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U41(z, z', z'') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(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__and(z, z') -{ 1 }-> mark(X) :|: z' = X, z = 1, X >= 0
   a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__isNat(z) -{ 1 }-> a__isNat(V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 1 }-> a__and(a__isNat(V1), 1 + 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__U21(a__and(a__isNat(M), 1 + N), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 1 }-> a__U11(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
   a__x(z, z') -{ 1 }-> a__U41(a__and(a__isNat(M), 1 + N), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__x(z, z') -{ 1 }-> a__U31(a__isNat(N)) :|: z = N, z' = 0, N >= 0
   a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + 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__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   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(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U21(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 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.

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

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U11(z0, z1) -> c1
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(z0, z1, z2) -> c4
   A__U31(tt) -> c5
   A__U31(z0) -> c6
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U41(z0, z1, z2) -> c10
   A__AND(tt, z0) -> c11(MARK(z0))
   A__AND(z0, z1) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(z0) -> c17
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c20
   A__X(z0, 0) -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, z1) -> c23
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(tt) -> c34
   MARK(s(z0)) -> c35(MARK(z0))
   MARK(0) -> c36
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U11(z0, z1) -> c1
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(z0, z1, z2) -> c4
   A__U31(tt) -> c5
   A__U31(z0) -> c6
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U41(z0, z1, z2) -> c10
   A__AND(tt, z0) -> c11(MARK(z0))
   A__AND(z0, z1) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(z0) -> c17
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c20
   A__X(z0, 0) -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, z1) -> c23
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(tt) -> c34
   MARK(s(z0)) -> c35(MARK(z0))
   MARK(0) -> c36
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U21_3, A__U31_1, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c1, c2_2, c3_2, c4, c5, c6, c7_3, c8_3, c9_2, c10, c11_1, c12, c13, c14_2, c15_1, c16_2, c17, c18_2, c19_3, c20, c21_2, c22_3, c23, c24_2, c25_2, c26_2, c27_2, c28_2, c29_2, c30_2, c31_2, c32_2, c33_1, c34, c35_1, c36


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

(47) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 12 trailing nodes:
   A__ISNAT(0) -> c13
   A__AND(z0, z1) -> c12
   A__U31(tt) -> c5
   A__U21(z0, z1, z2) -> c4
   A__X(z0, z1) -> c23
   A__U41(z0, z1, z2) -> c10
   MARK(0) -> c36
   A__ISNAT(z0) -> c17
   A__PLUS(z0, z1) -> c20
   A__U11(z0, z1) -> c1
   MARK(tt) -> c34
   A__U31(z0) -> c6

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, 0) -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, 0) -> c21(A__U31(a__isNat(z0)), A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U31(z0)) -> c28(A__U31(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U21_3, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c2_2, c3_2, c7_3, c8_3, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c21_2, c22_3, c24_2, c25_2, c26_2, c27_2, c28_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1


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

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U21_3, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c2_2, c3_2, c7_3, c8_3, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1


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

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

(52)
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__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))

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

   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0

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

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

(54)
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__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0

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

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

(56)
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, z0) -> c(MARK(z0)) [1]
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1]
   A__AND(tt, z0) -> c11(MARK(z0)) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1]
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) [1]
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1]
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1]
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1]
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c33(A__ISNAT(z0)) [1]
   MARK(s(z0)) -> c35(MARK(z0)) [1]
   A__X(z0, 0) -> c21(A__ISNAT(z0)) [1]
   MARK(U31(z0)) -> c28(MARK(z0)) [1]
   a__U11(tt, z0) -> mark(z0) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U21(z0, z1, z2) -> U21(z0, z1, z2) [0]
   a__U31(tt) -> 0 [0]
   a__U31(z0) -> U31(z0) [0]
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNat(0) -> tt [0]
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1)) [0]
   a__isNat(s(z0)) -> a__isNat(z0) [0]
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1)) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) [0]
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   a__x(z0, 0) -> a__U31(a__isNat(z0)) [0]
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0]
   a__x(z0, z1) -> x(z0, z1) [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(U31(z0)) -> a__U31(mark(z0)) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), z1) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]

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

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

(58)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   A__U11(tt, z0) -> c(MARK(z0)) [1]
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1]
   A__AND(tt, z0) -> c11(MARK(z0)) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1]
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) [1]
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1]
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1]
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1]
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c33(A__ISNAT(z0)) [1]
   MARK(s(z0)) -> c35(MARK(z0)) [1]
   A__X(z0, 0) -> c21(A__ISNAT(z0)) [1]
   MARK(U31(z0)) -> c28(MARK(z0)) [1]
   a__U11(tt, z0) -> mark(z0) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U21(z0, z1, z2) -> U21(z0, z1, z2) [0]
   a__U31(tt) -> 0 [0]
   a__U31(z0) -> U31(z0) [0]
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNat(0) -> tt [0]
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1)) [0]
   a__isNat(s(z0)) -> a__isNat(z0) [0]
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1)) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) [0]
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   a__x(z0, 0) -> a__U31(a__isNat(z0)) [0]
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0]
   a__x(z0, z1) -> x(z0, z1) [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(U31(z0)) -> a__U31(mark(z0)) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), z1) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]

The TRS has the following type information:
A__U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> c
tt :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c
MARK :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
A__U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> c2:c3
c2 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c2:c3
A__PLUS :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> c18:c19
mark :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c3 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c2:c3
A__U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> c7:c8:c9
c7 :: c18:c19 -> c22:c21 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c7:c8:c9
a__x :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
A__X :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> c22:c21
c8 :: c18:c19 -> c22:c21 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c7:c8:c9
c9 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c7:c8:c9
A__AND :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> c11
c11 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c11
A__ISNAT :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> c14:c15:c16
plus :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c14 :: c11 -> c14:c15:c16 -> c14:c15:c16
a__isNat :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
isNat :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
s :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c15 :: c14:c15:c16 -> c14:c15:c16
x :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c16 :: c11 -> c14:c15:c16 -> c14:c15:c16
0 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c18 :: c -> c14:c15:c16 -> c18:c19
c19 :: c2:c3 -> c11 -> c14:c15:c16 -> c18:c19
a__and :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c22 :: c7:c8:c9 -> c11 -> c14:c15:c16 -> c22:c21
U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c24 :: c -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c25 :: c2:c3 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c26 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c27 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c29 :: c7:c8:c9 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c30 :: c22:c21 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c31 :: c22:c21 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
and :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c32 :: c11 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c33 :: c14:c15:c16 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c35 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c21 :: c14:c15:c16 -> c22:c21
U31 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
c28 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
a__U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
a__U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
a__plus :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
a__U31 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31
a__U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31 -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31

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

(59) 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__U11_2
   A__U21_3
   A__U41_3
   A__AND_2
   A__ISNAT_1
   A__PLUS_2
   A__X_2
   MARK_1

(c) The following functions are completely defined:

   a__U11_2
   a__U21_3
   a__U31_1
   a__U41_3
   a__and_2
   a__isNat_1
   a__plus_2
   a__x_2
   mark_1

Due to the following rules being added:

   a__U11(v0, v1) -> null_a__U11 [0]
   a__U21(v0, v1, v2) -> null_a__U21 [0]
   a__U31(v0) -> null_a__U31 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__plus(v0, v1) -> null_a__plus [0]
   a__x(v0, v1) -> null_a__x [0]
   mark(v0) -> null_mark [0]

And the following fresh constants:    null_a__U11, null_a__U21, null_a__U31, null_a__U41, null_a__and, null_a__isNat, null_a__plus, null_a__x, null_mark, const, const1, const2, const3, const4, const5, const6, const7

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

(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__U11(tt, z0) -> c(MARK(z0)) [1]
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1]
   A__AND(tt, z0) -> c11(MARK(z0)) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1]
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) [1]
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1]
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1]
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1]
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c33(A__ISNAT(z0)) [1]
   MARK(s(z0)) -> c35(MARK(z0)) [1]
   A__X(z0, 0) -> c21(A__ISNAT(z0)) [1]
   MARK(U31(z0)) -> c28(MARK(z0)) [1]
   a__U11(tt, z0) -> mark(z0) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U21(z0, z1, z2) -> U21(z0, z1, z2) [0]
   a__U31(tt) -> 0 [0]
   a__U31(z0) -> U31(z0) [0]
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNat(0) -> tt [0]
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1)) [0]
   a__isNat(s(z0)) -> a__isNat(z0) [0]
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1)) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) [0]
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   a__x(z0, 0) -> a__U31(a__isNat(z0)) [0]
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0]
   a__x(z0, z1) -> x(z0, z1) [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(U31(z0)) -> a__U31(mark(z0)) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), z1) [0]
   mark(isNat(z0)) -> a__isNat(z0) [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__U21(v0, v1, v2) -> null_a__U21 [0]
   a__U31(v0) -> null_a__U31 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__plus(v0, v1) -> null_a__plus [0]
   a__x(v0, v1) -> null_a__x [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c
tt :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c
MARK :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
A__U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c2:c3
c2 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c2:c3
A__PLUS :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c18:c19
mark :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c3 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c2:c3
A__U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c7:c8:c9
c7 :: c18:c19 -> c22:c21 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c7:c8:c9
a__x :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
A__X :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c22:c21
c8 :: c18:c19 -> c22:c21 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c7:c8:c9
c9 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c7:c8:c9
A__AND :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c11
c11 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c11
A__ISNAT :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c14:c15:c16
plus :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c14 :: c11 -> c14:c15:c16 -> c14:c15:c16
a__isNat :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
isNat :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
s :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c15 :: c14:c15:c16 -> c14:c15:c16
x :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c16 :: c11 -> c14:c15:c16 -> c14:c15:c16
0 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c18 :: c -> c14:c15:c16 -> c18:c19
c19 :: c2:c3 -> c11 -> c14:c15:c16 -> c18:c19
a__and :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c22 :: c7:c8:c9 -> c11 -> c14:c15:c16 -> c22:c21
U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c24 :: c -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c25 :: c2:c3 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c26 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c27 :: c18:c19 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c29 :: c7:c8:c9 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c30 :: c22:c21 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c31 :: c22:c21 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
and :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c32 :: c11 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c33 :: c14:c15:c16 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c35 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
c21 :: c14:c15:c16 -> c22:c21
U31 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c28 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
a__U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
a__U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
a__plus :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
a__U31 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
a__U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__U31 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__and :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__isNat :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__plus :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__x :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_mark :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
const :: c
const1 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28
const2 :: c2:c3
const3 :: c18:c19
const4 :: c7:c8:c9
const5 :: c22:c21
const6 :: c11
const7 :: c14:c15:c16

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

(61) 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__U21(v0, v1, v2) -> null_a__U21 [0]
   a__U31(v0) -> null_a__U31 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__plus(v0, v1) -> null_a__plus [0]
   a__x(v0, v1) -> null_a__x [0]
   mark(v0) -> null_mark [0]
   A__U11(v0, v1) -> null_A__U11 [0]
   A__U21(v0, v1, v2) -> null_A__U21 [0]
   A__U41(v0, v1, v2) -> null_A__U41 [0]
   A__AND(v0, v1) -> null_A__AND [0]
   A__ISNAT(v0) -> null_A__ISNAT [0]
   A__PLUS(v0, v1) -> null_A__PLUS [0]
   A__X(v0, v1) -> null_A__X [0]
   MARK(v0) -> null_MARK [0]

And the following fresh constants:    null_a__U11, null_a__U21, null_a__U31, null_a__U41, null_a__and, null_a__isNat, null_a__plus, null_a__x, null_mark, null_A__U11, null_A__U21, null_A__U41, null_A__AND, null_A__ISNAT, null_A__PLUS, null_A__X, null_MARK

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

(62)
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, z0) -> c(MARK(z0)) [1]
   A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1]
   A__AND(tt, z0) -> c11(MARK(z0)) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1]
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) [1]
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1]
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1]
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1]
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c33(A__ISNAT(z0)) [1]
   MARK(s(z0)) -> c35(MARK(z0)) [1]
   A__X(z0, 0) -> c21(A__ISNAT(z0)) [1]
   MARK(U31(z0)) -> c28(MARK(z0)) [1]
   a__U11(tt, z0) -> mark(z0) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U21(z0, z1, z2) -> U21(z0, z1, z2) [0]
   a__U31(tt) -> 0 [0]
   a__U31(z0) -> U31(z0) [0]
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNat(0) -> tt [0]
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1)) [0]
   a__isNat(s(z0)) -> a__isNat(z0) [0]
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1)) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) [0]
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   a__x(z0, 0) -> a__U31(a__isNat(z0)) [0]
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0]
   a__x(z0, z1) -> x(z0, z1) [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(U31(z0)) -> a__U31(mark(z0)) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), z1) [0]
   mark(isNat(z0)) -> a__isNat(z0) [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__U21(v0, v1, v2) -> null_a__U21 [0]
   a__U31(v0) -> null_a__U31 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__plus(v0, v1) -> null_a__plus [0]
   a__x(v0, v1) -> null_a__x [0]
   mark(v0) -> null_mark [0]
   A__U11(v0, v1) -> null_A__U11 [0]
   A__U21(v0, v1, v2) -> null_A__U21 [0]
   A__U41(v0, v1, v2) -> null_A__U41 [0]
   A__AND(v0, v1) -> null_A__AND [0]
   A__ISNAT(v0) -> null_A__ISNAT [0]
   A__PLUS(v0, v1) -> null_A__PLUS [0]
   A__X(v0, v1) -> null_A__X [0]
   MARK(v0) -> null_MARK [0]

The TRS has the following type information:
A__U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c:null_A__U11
tt :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c:null_A__U11
MARK :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
A__U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c2:c3:null_A__U21
c2 :: c18:c19:null_A__PLUS -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c2:c3:null_A__U21
A__PLUS :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c18:c19:null_A__PLUS
mark :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c3 :: c18:c19:null_A__PLUS -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c2:c3:null_A__U21
A__U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c7:c8:c9:null_A__U41
c7 :: c18:c19:null_A__PLUS -> c22:c21:null_A__X -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c7:c8:c9:null_A__U41
a__x :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
A__X :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c22:c21:null_A__X
c8 :: c18:c19:null_A__PLUS -> c22:c21:null_A__X -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c7:c8:c9:null_A__U41
c9 :: c18:c19:null_A__PLUS -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c7:c8:c9:null_A__U41
A__AND :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c11:null_A__AND
c11 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c11:null_A__AND
A__ISNAT :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> c14:c15:c16:null_A__ISNAT
plus :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c14 :: c11:null_A__AND -> c14:c15:c16:null_A__ISNAT -> c14:c15:c16:null_A__ISNAT
a__isNat :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
isNat :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
s :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c15 :: c14:c15:c16:null_A__ISNAT -> c14:c15:c16:null_A__ISNAT
x :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c16 :: c11:null_A__AND -> c14:c15:c16:null_A__ISNAT -> c14:c15:c16:null_A__ISNAT
0 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c18 :: c:null_A__U11 -> c14:c15:c16:null_A__ISNAT -> c18:c19:null_A__PLUS
c19 :: c2:c3:null_A__U21 -> c11:null_A__AND -> c14:c15:c16:null_A__ISNAT -> c18:c19:null_A__PLUS
a__and :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c22 :: c7:c8:c9:null_A__U41 -> c11:null_A__AND -> c14:c15:c16:null_A__ISNAT -> c22:c21:null_A__X
U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c24 :: c:null_A__U11 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c25 :: c2:c3:null_A__U21 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
c26 :: c18:c19:null_A__PLUS -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
c27 :: c18:c19:null_A__PLUS -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c29 :: c7:c8:c9:null_A__U41 -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
c30 :: c22:c21:null_A__X -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
c31 :: c22:c21:null_A__X -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
and :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c32 :: c11:null_A__AND -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
c33 :: c14:c15:c16:null_A__ISNAT -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
c35 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
c21 :: c14:c15:c16:null_A__ISNAT -> c22:c21:null_A__X
U31 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
c28 :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK -> c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK
a__U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
a__U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
a__plus :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
a__U31 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
a__U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__U11 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__U21 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__U31 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__U41 :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__and :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__isNat :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__plus :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_a__x :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_mark :: tt:plus:isNat:s:x:0:U11:U21:U41:and:U31:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__and:null_a__isNat:null_a__plus:null_a__x:null_mark
null_A__U11 :: c:null_A__U11
null_A__U21 :: c2:c3:null_A__U21
null_A__U41 :: c7:c8:c9:null_A__U41
null_A__AND :: c11:null_A__AND
null_A__ISNAT :: c14:c15:c16:null_A__ISNAT
null_A__PLUS :: c18:c19:null_A__PLUS
null_A__X :: c22:c21:null_A__X
null_MARK :: c24:c25:c26:c27:c29:c30:c31:c32:c33:c35:c28:null_MARK

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

(63) 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__U21 => 0
   null_a__U31 => 0
   null_a__U41 => 0
   null_a__and => 0
   null_a__isNat => 0
   null_a__plus => 0
   null_a__x => 0
   null_mark => 0
   null_A__U11 => 0
   null_A__U21 => 0
   null_A__U41 => 0
   null_A__AND => 0
   null_A__ISNAT => 0
   null_A__PLUS => 0
   null_A__X => 0
   null_MARK => 0

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

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

   A__AND(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0
   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__AND(a__isNat(z0), 1 + 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__U11(a__isNat(z0), z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__isNat(z1), 1 + z0), z1, z0) + A__AND(a__isNat(z1), 1 + z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   A__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__U11(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0
   A__U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__U21(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U21(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(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'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + A__X(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + A__X(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__X(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__X(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0
   A__X(z, z') -{ 1 }-> 1 + A__U41(a__and(a__isNat(z1), 1 + z0), z1, z0) + A__AND(a__isNat(z1), 1 + z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + 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__X(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   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__U21(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   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
   MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z') -{ 0 }-> mark(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__U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U21(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U21(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U31(z) -{ 0 }-> 0 :|: z = 1
   a__U31(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U31(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__plus(a__x(mark(z1), mark(z0)), mark(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__and(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0
   a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__isNat(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__and(a__isNat(z0), 1 + 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__U21(a__and(a__isNat(z1), 1 + z0), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__plus(z, z') -{ 0 }-> a__U11(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
   a__x(z, z') -{ 0 }-> a__U41(a__and(a__isNat(z1), 1 + z0), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__x(z, z') -{ 0 }-> a__U31(a__isNat(z0)) :|: z = z0, z0 >= 0, z' = 0
   a__x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__x(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   mark(z) -{ 0 }-> a__x(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   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__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   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)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U21(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 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.

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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by 
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U21_3, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c3_2, c7_3, c8_3, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2


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

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U21_3, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c3_2, c7_3, c8_3, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by 
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3

Compound Symbols:   c_1, c7_3, c8_3, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2


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

(71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U21(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3

Compound Symbols:   c_1, c7_3, c8_3, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3

Compound Symbols:   c_1, c7_3, c8_3, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) by 
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(0))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(0))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(0))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(0))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3

Compound Symbols:   c_1, c8_3, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3


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

(77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing tuple parts
----------------------------------------

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3

Compound Symbols:   c_1, c8_3, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2


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(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) by 
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(tt))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(0))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(tt))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(0))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(tt))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(0))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3

Compound Symbols:   c_1, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3


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

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U41_3, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3

Compound Symbols:   c_1, c9_2, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2


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(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) by 
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3, A__U41_3

Compound Symbols:   c_1, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2


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

(85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3, A__U41_3

Compound Symbols:   c_1, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2


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

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3, A__U41_3

Compound Symbols:   c_1, c11_1, c14_2, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNAT(plus(z0, z1)) -> c14(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) by 
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)), A__ISNAT(0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__AND(isNat(z0), isNat(x1)), A__ISNAT(z0))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)), A__ISNAT(0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__AND(isNat(z0), isNat(x1)), A__ISNAT(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)), A__ISNAT(0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__AND(isNat(z0), isNat(x1)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3, A__U41_3

Compound Symbols:   c_1, c11_1, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2


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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3, A__U41_3

Compound Symbols:   c_1, c11_1, c15_1, c16_2, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNAT(x(z0, z1)) -> c16(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) by 
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)), A__ISNAT(0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(z0, x1)) -> c16(A__AND(isNat(z0), isNat(x1)), A__ISNAT(z0))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)), A__ISNAT(0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(z0, x1)) -> c16(A__AND(isNat(z0), isNat(x1)), A__ISNAT(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)), A__ISNAT(0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(z0, x1)) -> c16(A__AND(isNat(z0), isNat(x1)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3, A__U41_3

Compound Symbols:   c_1, c11_1, c15_1, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2


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

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3, A__U41_3

Compound Symbols:   c_1, c11_1, c15_1, c18_2, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__PLUS(z0, 0) -> c18(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) by 
   A__PLUS(0, 0) -> c18(A__U11(tt, 0), A__ISNAT(0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(z0, 0) -> c18(A__U11(isNat(z0), z0), A__ISNAT(z0))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0), A__ISNAT(0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(z0, 0) -> c18(A__U11(isNat(z0), z0), A__ISNAT(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0), A__ISNAT(0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(z0, 0) -> c18(A__U11(isNat(z0), z0), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3, A__U41_3

Compound Symbols:   c_1, c11_1, c15_1, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2


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

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U21_3, A__U41_3

Compound Symbols:   c_1, c11_1, c15_1, c19_3, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1


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

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__PLUS(z0, s(z1)) -> c19(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) by 
   A__PLUS(x0, s(x1)) -> c19(A__U21(and(a__isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)), A__ISNAT(0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__U21(and(a__isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)), A__ISNAT(0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__U21(and(a__isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)), A__ISNAT(0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__X_2, MARK_1, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3


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

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, A__X_2, MARK_1, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c22_3, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__X(z0, s(z1)) -> c22(A__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) by 
   A__X(x0, s(x1)) -> c22(A__U41(and(a__isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)), A__ISNAT(0))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(x1)) -> c22(A__U41(and(a__isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)), A__ISNAT(0))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(x1)) -> c22(A__U41(and(a__isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)), A__ISNAT(0))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3


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

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c24_2, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U11(z0, z1)) -> c24(A__U11(mark(z0), z1), MARK(z0)) by 
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c24(A__U11(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U11(0, x1)) -> c24(A__U11(0, x1), MARK(0))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c24(A__U11(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U11(0, x1)) -> c24(A__U11(0, x1), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c24(A__U11(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U11(0, x1)) -> c24(A__U11(0, x1), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2


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

(111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U11(0, x1)) -> c24(A__U11(0, x1), MARK(0))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c24(A__U11(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c24(A__U11(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2


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

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c25_2, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1


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(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U21(z0, z1, z2)) -> c25(A__U21(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c25(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U21(0, x1, x2)) -> c25(A__U21(0, x1, x2), MARK(0))

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(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c25(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U21(0, x1, x2)) -> c25(A__U21(0, x1, x2), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c25(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U21(0, x1, x2)) -> c25(A__U21(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2


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

(117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U21(0, x1, x2)) -> c25(A__U21(0, x1, x2), MARK(0))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c25(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c25(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2


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

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c26_2, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1


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

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(plus(z0, z1)) -> c26(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, tt)) -> c26(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)), MARK(0))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, tt)) -> c26(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, tt)) -> c26(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2


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

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c27_2, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2


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

(127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(tt))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2


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

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c29_2, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U41(z0, z1, z2)) -> c29(A__U41(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c29(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(0, x1, x2)) -> c29(A__U41(0, x1, x2), MARK(0))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c29(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(0, x1, x2)) -> c29(A__U41(0, x1, x2), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c29(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(0, x1, x2)) -> c29(A__U41(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2


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

(133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U41(0, x1, x2)) -> c29(A__U41(0, x1, x2), MARK(0))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c29(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c29(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2


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

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c30_2, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1


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

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(x(z0, z1)) -> c30(A__X(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, tt)) -> c30(A__X(mark(x0), tt), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)), MARK(tt))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)), MARK(0))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, tt)) -> c30(A__X(mark(x0), tt), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)), MARK(tt))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, tt)) -> c30(A__X(mark(x0), tt), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)), MARK(tt))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2


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

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c31_2, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(x(z0, z1)) -> c31(A__X(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, tt)) -> c31(A__X(mark(x0), tt), MARK(tt))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0), MARK(0))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
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   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
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   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
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   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
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   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
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   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, tt)) -> c31(A__X(mark(x0), tt), MARK(tt))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0), MARK(0))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, tt)) -> c31(A__X(mark(x0), tt), MARK(tt))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0), MARK(0))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2


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

(143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(x(x0, tt)) -> c31(A__X(mark(x0), tt), MARK(tt))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0), MARK(0))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
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   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2


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

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
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   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
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   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c32_2, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1


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

(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(and(z0, z1)) -> c32(A__AND(mark(z0), z1), MARK(z0)) by 
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c32(A__AND(s(mark(z0)), x1), MARK(s(z0)))
   MARK(and(0, x1)) -> c32(A__AND(0, x1), MARK(0))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c32(A__AND(s(mark(z0)), x1), MARK(s(z0)))
   MARK(and(0, x1)) -> c32(A__AND(0, x1), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c32(A__AND(s(mark(z0)), x1), MARK(s(z0)))
   MARK(and(0, x1)) -> c32(A__AND(0, x1), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2


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

(149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(and(0, x1)) -> c32(A__AND(0, x1), MARK(0))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
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   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
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   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
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   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c32(A__AND(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U21(isNat(z0), x1, x2)) -> c25(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c32(A__AND(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2


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

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c32(MARK(s(z0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
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   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
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   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
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   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c32(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) by 
   A__U21(tt, U11(x0, z1), x2) -> c2(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
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   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
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   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
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   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
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   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
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   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c32(MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
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   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c32(MARK(s(z0)))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(157) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) by 
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(x3))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(tt))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(0))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
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   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(x3))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(tt))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
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   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
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   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c26(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U31(z0), x1)) -> c26(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c26(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c26(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(and(z0, z1), x1)) -> c26(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(s(z0), x1)) -> c26(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c26(MARK(x0))
   MARK(plus(tt, x1)) -> c26(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c26(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U31(z0))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c27(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, and(z0, z1))) -> c27(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c27(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0), x1)) -> c27(A__PLUS(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c27(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(and(z0, z1), x1)) -> c27(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0))
   MARK(U41(U11(z0, z1), x1, x2)) -> c29(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U21(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c29(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(U31(z0), x1, x2)) -> c29(A__U41(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c29(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(x(z0, z1), x1, x2)) -> c29(A__U41(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c29(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNat(z0), x1, x2)) -> c29(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(tt, x1, x2)) -> c29(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c29(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1))) -> c30(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c32(MARK(s(z0)))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(x3))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(tt))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
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   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
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   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
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   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
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   MARK(x(x0, U21(z0, z1, z2))) -> c30(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c30(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U31(z0))) -> c30(A__X(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(x(x0, U41(z0, z1, z2))) -> c30(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c30(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, and(z0, z1))) -> c30(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(x(x0, isNat(z0))) -> c30(A__X(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(x(x0, s(z0))) -> c30(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c30(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1), x1)) -> c30(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c30(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c30(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U31(z0), x1)) -> c30(A__X(a__U31(mark(z0)), mark(x1)), MARK(U31(z0)))
   MARK(x(U41(z0, z1, z2), x1)) -> c30(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c30(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(and(z0, z1), x1)) -> c30(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(x(isNat(z0), x1)) -> c30(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(x(s(z0), x1)) -> c30(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c30(MARK(x0))
   MARK(x(tt, x1)) -> c30(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c30(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1))) -> c31(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c31(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c31(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U31(z0))) -> c31(A__X(mark(x0), a__U31(mark(z0))), MARK(U31(z0)))
   MARK(x(x0, U41(z0, z1, z2))) -> c31(A__X(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c31(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, and(z0, z1))) -> c31(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(x(x0, isNat(z0))) -> c31(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(x(x0, s(z0))) -> c31(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1), x1)) -> c31(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c31(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c31(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U31(z0), x1)) -> c31(A__X(a__U31(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(U41(z0, z1, z2), x1)) -> c31(A__X(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c31(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(and(z0, z1), x1)) -> c31(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(x(isNat(z0), x1)) -> c31(A__X(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c31(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c31(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c31(A__X(0, mark(x1)), MARK(x1))
   MARK(x(x0, 0)) -> c31(A__X(mark(x0), 0))
   MARK(and(U11(z0, z1), x1)) -> c32(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U21(z0, z1, z2), x1)) -> c32(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(and(plus(z0, z1), x1)) -> c32(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(and(U31(z0), x1)) -> c32(A__AND(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c32(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(x(z0, z1), x1)) -> c32(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c32(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNat(z0), x1)) -> c32(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(tt, x1)) -> c32(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c32(MARK(s(z0)))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
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   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(161) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) by 
   A__U21(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
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   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U21(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
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   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U21(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
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   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, U31(z0), x1) -> c2(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(x1)) by 
   A__U21(tt, U31(x0), x1) -> c2(A__PLUS(mark(x1), U31(mark(x0))), MARK(x1))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))), MARK(tt))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))), MARK(0))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
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   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(x0), x1) -> c2(A__PLUS(mark(x1), U31(mark(x0))), MARK(x1))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))), MARK(tt))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
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   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(x0), x1) -> c2(A__PLUS(mark(x1), U31(mark(x0))), MARK(x1))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))), MARK(tt))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
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   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
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   MARK(and(tt, x1)) -> c32(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c32(MARK(s(z0)))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, U41(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) by 
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
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   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
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   A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(173) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) by 
   A__U21(tt, x(x0, x1), x2) -> c2(A__PLUS(mark(x2), x(mark(x0), mark(x1))), MARK(x2))
   A__U21(tt, x(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(tt))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(0))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(tt))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U21(tt, x(x0, x1), x2) -> c2(A__PLUS(mark(x2), x(mark(x0), mark(x1))), MARK(x2))
   A__U21(tt, x(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(tt))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
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   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
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   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U21(tt, x(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(177) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) by 
   A__U21(tt, and(x0, z1), x2) -> c2(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)), MARK(0))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U21(tt, x(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(x0, z1), x2) -> c2(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
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   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
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   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
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   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
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   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
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   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
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   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(x0, z1), x2) -> c2(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
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   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
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   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
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   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U21(tt, x(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(181) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) by 
   A__U21(tt, isNat(0), x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)), MARK(tt))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)), MARK(0))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U21(tt, x(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(0), x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)), MARK(tt))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)), MARK(0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
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   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
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   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
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   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
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   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
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   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(0), x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)), MARK(tt))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
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   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
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   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
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   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
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   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(185) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) by 
   A__U21(tt, U11(z0, z1), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U11(x1, x2)))
   A__U21(tt, U21(z0, z1, z2), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__U21(mark(z0), z1, z2)), MARK(U11(x1, x2)))
   A__U21(tt, plus(z0, z1), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U11(x1, x2)))
   A__U21(tt, U31(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__U31(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, U41(z0, z1, z2), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U11(x1, x2)))
   A__U21(tt, x(z0, z1), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__x(mark(z0), mark(z1))), MARK(U11(x1, x2)))
   A__U21(tt, and(z0, z1), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__and(mark(z0), z1)), MARK(U11(x1, x2)))
   A__U21(tt, isNat(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__isNat(z0)), MARK(U11(x1, x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2)))

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
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   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
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   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
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   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
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   MARK(plus(x0, 0)) -> c26(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c26(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
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   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
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   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
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   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
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   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
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   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
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   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
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   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
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   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
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   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
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   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
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   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
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   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(189) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) by 
   A__U21(tt, U11(z0, z1), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U11(mark(z0), z1)), MARK(U21(x1, x2, x3)))
   A__U21(tt, U21(z0, z1, z2), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U21(x1, x2, x3)))
   A__U21(tt, plus(z0, z1), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U21(x1, x2, x3)))
   A__U21(tt, U31(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U31(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, U41(z0, z1, z2), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U21(x1, x2, x3)))
   A__U21(tt, x(z0, z1), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(U21(x1, x2, x3)))
   A__U21(tt, and(z0, z1), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(U21(x1, x2, x3)))
   A__U21(tt, isNat(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__isNat(z0)), MARK(U21(x1, x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(U21(x1, x2, x3)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(U21(0, x2, x3)))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
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   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(U21(x1, x2, x3)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(U21(0, x2, x3)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
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   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
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   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
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   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
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   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
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   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
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   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
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   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
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   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
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   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
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   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
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   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U21(tt, x(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
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   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
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   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
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   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
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   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(U21(x1, x2, x3)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(U21(0, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
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   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
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   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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(193) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) by 
   A__U21(tt, U11(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1)), MARK(plus(x1, x2)))
   A__U21(tt, U21(z0, z1, z2), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U21(tt, plus(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(x1, x2)))
   A__U21(tt, U31(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U31(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, U41(z0, z1, z2), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U41(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U21(tt, x(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__x(mark(z0), mark(z1))), MARK(plus(x1, x2)))
   A__U21(tt, and(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__and(mark(z0), z1)), MARK(plus(x1, x2)))
   A__U21(tt, isNat(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNat(z0)), MARK(plus(x1, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))

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

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
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   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
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   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
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   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
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   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
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   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
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   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U21(tt, x(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
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   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
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   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
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   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
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   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
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   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
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   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0)))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(197) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(U31(z0))) by 
   A__U21(tt, U11(z0, z1), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), a__U11(mark(z0), z1)), MARK(U31(x1)))
   A__U21(tt, U21(z0, z1, z2), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), a__U21(mark(z0), z1, z2)), MARK(U31(x1)))
   A__U21(tt, plus(z0, z1), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U31(x1)))
   A__U21(tt, U31(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), a__U31(mark(z0))), MARK(U31(x1)))
   A__U21(tt, U41(z0, z1, z2), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U31(x1)))
   A__U21(tt, x(z0, z1), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), a__x(mark(z0), mark(z1))), MARK(U31(x1)))
   A__U21(tt, and(z0, z1), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), a__and(mark(z0), z1)), MARK(U31(x1)))
   A__U21(tt, isNat(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), a__isNat(z0)), MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), tt), MARK(U31(x1)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
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   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
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   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
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   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
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   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, tt, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), tt), MARK(U31(x1)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
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   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, tt, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), tt), MARK(U31(x1)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
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   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
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   MARK(plus(U21(z0, z1, z2), x1)) -> c26(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
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   MARK(plus(isNat(z0), x1)) -> c26(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
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   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
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   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(201) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) by 
   A__U21(tt, U11(z0, z1), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), a__U11(mark(z0), z1)), MARK(U41(x1, x2, x3)))
   A__U21(tt, U21(z0, z1, z2), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U41(x1, x2, x3)))
   A__U21(tt, plus(z0, z1), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U41(x1, x2, x3)))
   A__U21(tt, U31(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), a__U31(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, U41(z0, z1, z2), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U41(x1, x2, x3)))
   A__U21(tt, x(z0, z1), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(U41(x1, x2, x3)))
   A__U21(tt, and(z0, z1), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(U41(x1, x2, x3)))
   A__U21(tt, isNat(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), a__isNat(z0)), MARK(U41(x1, x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3)))

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
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   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
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   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
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   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
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   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
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   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(205) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) by 
   A__U21(tt, U11(z0, z1), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__U11(mark(z0), z1)), MARK(x(x1, x2)))
   A__U21(tt, U21(z0, z1, z2), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__U21(mark(z0), z1, z2)), MARK(x(x1, x2)))
   A__U21(tt, plus(z0, z1), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(x(x1, x2)))
   A__U21(tt, U31(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__U31(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, U41(z0, z1, z2), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__U41(mark(z0), z1, z2)), MARK(x(x1, x2)))
   A__U21(tt, x(z0, z1), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__x(mark(z0), mark(z1))), MARK(x(x1, x2)))
   A__U21(tt, and(z0, z1), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__and(mark(z0), z1)), MARK(x(x1, x2)))
   A__U21(tt, isNat(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__isNat(z0)), MARK(x(x1, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), tt), MARK(x(x1, x2)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))

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

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
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   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, tt, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), tt), MARK(x(x1, x2)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
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   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
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   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
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   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
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   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
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   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
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   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
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   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
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   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
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   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
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   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
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   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
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   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
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   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
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   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
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   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, tt, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), tt), MARK(x(x1, x2)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
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   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1)))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
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   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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(209) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) by 
   A__U21(tt, U11(z0, z1), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__U11(mark(z0), z1)), MARK(and(x1, x2)))
   A__U21(tt, U21(z0, z1, z2), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__U21(mark(z0), z1, z2)), MARK(and(x1, x2)))
   A__U21(tt, plus(z0, z1), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(and(x1, x2)))
   A__U21(tt, U31(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__U31(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, U41(z0, z1, z2), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(and(x1, x2)))
   A__U21(tt, x(z0, z1), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__x(mark(z0), mark(z1))), MARK(and(x1, x2)))
   A__U21(tt, and(z0, z1), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__and(mark(z0), z1)), MARK(and(x1, x2)))
   A__U21(tt, isNat(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__isNat(z0)), MARK(and(x1, x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2)))

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

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
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   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
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   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
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   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
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   A__U21(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__isNat(z0), mark(x1))), MARK(x2))
   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U31(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U21(tt, and(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__x(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2))
   A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2))
   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
   A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2))
   A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2)))
   A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U21(tt, and(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__and(mark(x0), x1)), MARK(U31(z0)))
   A__U21(tt, and(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U21(tt, and(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(x(z0, z1)))
   A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1)))
   A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0)))
   A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0)))
   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
   A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
   A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2)))
   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
   A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1)))
   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
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   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
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   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(213) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) by 
   A__U21(tt, U11(z0, z1), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__U11(mark(z0), z1)), MARK(isNat(x1)))
   A__U21(tt, U21(z0, z1, z2), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__U21(mark(z0), z1, z2)), MARK(isNat(x1)))
   A__U21(tt, plus(z0, z1), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__plus(mark(z0), mark(z1))), MARK(isNat(x1)))
   A__U21(tt, U31(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__U31(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, U41(z0, z1, z2), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__U41(mark(z0), z1, z2)), MARK(isNat(x1)))
   A__U21(tt, x(z0, z1), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__x(mark(z0), mark(z1))), MARK(isNat(x1)))
   A__U21(tt, and(z0, z1), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__and(mark(z0), z1)), MARK(isNat(x1)))
   A__U21(tt, isNat(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__isNat(z0)), MARK(isNat(x1)))
   A__U21(tt, tt, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))

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

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
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   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, tt, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
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   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
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   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
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   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
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   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
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   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
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   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
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   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
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   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, tt, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
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   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
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   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
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   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
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   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
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   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
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   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
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   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
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   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
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   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(217) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) by 
   A__U21(tt, U11(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U11(mark(z0), z1)), MARK(s(x1)))
   A__U21(tt, U21(z0, z1, z2), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U21(mark(z0), z1, z2)), MARK(s(x1)))
   A__U21(tt, plus(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(s(x1)))
   A__U21(tt, U31(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U31(mark(z0))), MARK(s(x1)))
   A__U21(tt, U41(z0, z1, z2), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(s(x1)))
   A__U21(tt, x(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__x(mark(z0), mark(z1))), MARK(s(x1)))
   A__U21(tt, and(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__and(mark(z0), z1)), MARK(s(x1)))
   A__U21(tt, isNat(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__isNat(z0)), MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))

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

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
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   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
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   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
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   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
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   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
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   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
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   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
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   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
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   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
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   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
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   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
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   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
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   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
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   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
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   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
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   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
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   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
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   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
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   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
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   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
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   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
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   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
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   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
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   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(221) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) by 
   A__U21(tt, U11(z0, z1), tt) -> c2(A__PLUS(tt, a__U11(mark(z0), z1)))
   A__U21(tt, U21(z0, z1, z2), tt) -> c2(A__PLUS(tt, a__U21(mark(z0), z1, z2)))
   A__U21(tt, plus(z0, z1), tt) -> c2(A__PLUS(tt, a__plus(mark(z0), mark(z1))))
   A__U21(tt, U31(z0), tt) -> c2(A__PLUS(tt, a__U31(mark(z0))))
   A__U21(tt, U41(z0, z1, z2), tt) -> c2(A__PLUS(tt, a__U41(mark(z0), z1, z2)))
   A__U21(tt, x(z0, z1), tt) -> c2(A__PLUS(tt, a__x(mark(z0), mark(z1))))
   A__U21(tt, and(z0, z1), tt) -> c2(A__PLUS(tt, a__and(mark(z0), z1)))
   A__U21(tt, isNat(z0), tt) -> c2(A__PLUS(tt, a__isNat(z0)))
   A__U21(tt, tt, tt) -> c2(A__PLUS(tt, tt))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))

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

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
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   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
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   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, tt) -> c2(A__PLUS(tt, tt))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
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   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
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   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
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   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
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   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
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   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
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   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
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   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
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   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
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   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
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   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
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   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
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   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
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   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
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   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
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   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, tt) -> c2(A__PLUS(tt, tt))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(223) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U21(tt, tt, tt) -> c2(A__PLUS(tt, tt))

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

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
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   A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
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   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
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   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
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   A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U21(tt, U31(U11(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U11(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(U21(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U21(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(U31(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U31(mark(z0)))), MARK(x1))
   A__U21(tt, U31(U41(z0, z1, z2)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U21(tt, U31(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__x(mark(z0), mark(z1)))), MARK(x1))
   A__U21(tt, U31(and(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__and(mark(z0), z1))), MARK(x1))
   A__U21(tt, U31(isNat(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(a__isNat(z0))), MARK(x1))
   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
   A__U21(tt, U31(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U21(z0, z1, z2)))
   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
   A__U21(tt, U41(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U21(tt, U41(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(U31(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__U31(mark(z0)), x1, x2)), MARK(x3))
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   A__U21(tt, U41(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U21(tt, U41(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__and(mark(z0), z1), x1, x2)), MARK(x3))
   A__U21(tt, U41(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U21(tt, U41(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U21(tt, U41(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U21(tt, U41(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
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   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
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   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(225) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) by 
   A__U21(tt, U11(z0, z1), 0) -> c2(A__PLUS(0, a__U11(mark(z0), z1)))
   A__U21(tt, U21(z0, z1, z2), 0) -> c2(A__PLUS(0, a__U21(mark(z0), z1, z2)))
   A__U21(tt, plus(z0, z1), 0) -> c2(A__PLUS(0, a__plus(mark(z0), mark(z1))))
   A__U21(tt, U31(z0), 0) -> c2(A__PLUS(0, a__U31(mark(z0))))
   A__U21(tt, U41(z0, z1, z2), 0) -> c2(A__PLUS(0, a__U41(mark(z0), z1, z2)))
   A__U21(tt, x(z0, z1), 0) -> c2(A__PLUS(0, a__x(mark(z0), mark(z1))))
   A__U21(tt, and(z0, z1), 0) -> c2(A__PLUS(0, a__and(mark(z0), z1)))
   A__U21(tt, isNat(z0), 0) -> c2(A__PLUS(0, a__isNat(z0)))
   A__U21(tt, tt, 0) -> c2(A__PLUS(0, tt))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))

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

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
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   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, tt, 0) -> c2(A__PLUS(0, tt))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
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   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, tt, 0) -> c2(A__PLUS(0, tt))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(227) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U21(tt, tt, 0) -> c2(A__PLUS(0, tt))

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

(228)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
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   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
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   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(229) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by 
   A__U21(tt, U11(x0, z1), x2) -> c3(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1)))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))

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

(230)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
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   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U21(tt, U11(x0, z1), x2) -> c3(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1)))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
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   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
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   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
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   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
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   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U21(tt, U11(x0, z1), x2) -> c3(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1)))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(232)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
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   A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
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   A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
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   A__U21(tt, U31(tt), x1) -> c2(A__PLUS(mark(x1), a__U31(tt)), MARK(x1))
   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
   A__U21(tt, U31(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0))), MARK(U11(z0, z1)))
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   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
   A__U21(tt, U31(x0), 0) -> c2(A__PLUS(0, a__U31(mark(x0))))
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   A__U21(tt, U41(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U31(z0)))
   A__U21(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U21(tt, U41(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(and(z0, z1)))
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   A__U21(tt, U41(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
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   A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2))
   A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)))
   A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)))
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   A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U21(tt, isNat(x(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1))
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   A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U21(tt, isNat(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__isNat(x0)), MARK(U31(z0)))
   A__U21(tt, isNat(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U21(tt, isNat(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1)))
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   A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
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   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
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   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
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   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
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   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
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   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
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   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
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   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(233) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) by 
   A__U21(tt, U21(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(U21(x0, z1, z2)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2)))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(U21(U31(z0), x1, x2)))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U21(U41(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2)))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2)))
   A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(U21(0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))

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

(234)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
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   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(U21(x0, z1, z2)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2)))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(U21(U31(z0), x1, x2)))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U21(U41(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2)))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2)))
   A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(U21(0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1, x2)) -> c25(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c25(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U31(z0), x1, x2)) -> c25(A__U21(a__U31(mark(z0)), x1, x2), MARK(U31(z0)))
   MARK(U21(U41(z0, z1, z2), x1, x2)) -> c25(A__U21(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c25(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(and(z0, z1), x1, x2)) -> c25(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
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   MARK(U21(tt, x1, x2)) -> c25(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c26(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c26(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U31(z0))) -> c26(A__PLUS(mark(x0), a__U31(mark(z0))), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c26(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c26(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, and(z0, z1))) -> c26(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c26(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, s(z0))) -> c26(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(U21(x0, z1, z2)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2)))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(U21(U31(z0), x1, x2)))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U21(U41(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2)))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2)))
   A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(U21(0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(236)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
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   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2)))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(U21(U31(z0), x1, x2)))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U21(U41(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2)))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2)))
   A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
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   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
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   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
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   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
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   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
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   A__U21(tt, U31(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__U31(s(mark(z0)))), MARK(x1))
   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
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   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
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   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
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   A__U21(tt, U41(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U21(tt, U41(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, U31(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U31(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, U41(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U21(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U21(tt, x(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__and(mark(z0), z1))), MARK(x2))
   A__U21(tt, x(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__isNat(z0))), MARK(x2))
   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U21(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U21(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U21(tt, x(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U21(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(U31(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U31(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(U41(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U21(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U21(tt, x(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__and(mark(z0), z1), mark(x1))), MARK(x2))
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   A__U21(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U21(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U21(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U21(tt, x(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U21(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U21(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U21(tt, x(x0, x1), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__x(mark(x0), mark(x1))), MARK(U31(z0)))
   A__U21(tt, x(x0, x1), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U21(tt, x(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__x(mark(x0), mark(x1))), MARK(and(z0, z1)))
   A__U21(tt, x(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__x(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U21(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U21(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U21(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U21(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
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   A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2))
   A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2))
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   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(z0), x1) -> c2(MARK(x1))
   A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)))
   A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)))
   A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U21(tt, x0, U11(U31(z0), x2)) -> c2(A__PLUS(a__U11(a__U31(mark(z0)), x2), mark(x0)), MARK(U11(U31(z0), x2)))
   A__U21(tt, x0, U11(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, U11(x(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(x(z0, z1), x2)))
   A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2)))
   A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2)))
   A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
   A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2)))
   A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U21(tt, s(z0), U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), s(mark(z0))), MARK(U31(x1)))
   A__U21(tt, 0, U31(x1)) -> c2(A__PLUS(a__U31(mark(x1)), 0), MARK(U31(x1)))
   A__U21(tt, x0, U31(x1)) -> c2(A__PLUS(U31(mark(x1)), mark(x0)), MARK(U31(x1)))
   A__U21(tt, x0, U31(U11(z0, z1))) -> c2(A__PLUS(a__U31(a__U11(mark(z0), z1)), mark(x0)), MARK(U31(U11(z0, z1))))
   A__U21(tt, x0, U31(U21(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(U31(U21(z0, z1, z2))))
   A__U21(tt, x0, U31(plus(z0, z1))) -> c2(A__PLUS(a__U31(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U31(plus(z0, z1))))
   A__U21(tt, x0, U31(U31(z0))) -> c2(A__PLUS(a__U31(a__U31(mark(z0))), mark(x0)), MARK(U31(U31(z0))))
   A__U21(tt, x0, U31(U41(z0, z1, z2))) -> c2(A__PLUS(a__U31(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U31(U41(z0, z1, z2))))
   A__U21(tt, x0, U31(x(z0, z1))) -> c2(A__PLUS(a__U31(a__x(mark(z0), mark(z1))), mark(x0)), MARK(U31(x(z0, z1))))
   A__U21(tt, x0, U31(and(z0, z1))) -> c2(A__PLUS(a__U31(a__and(mark(z0), z1)), mark(x0)), MARK(U31(and(z0, z1))))
   A__U21(tt, x0, U31(isNat(z0))) -> c2(A__PLUS(a__U31(a__isNat(z0)), mark(x0)), MARK(U31(isNat(z0))))
   A__U21(tt, x0, U31(tt)) -> c2(A__PLUS(a__U31(tt), mark(x0)), MARK(U31(tt)))
   A__U21(tt, x0, U31(s(z0))) -> c2(A__PLUS(a__U31(s(mark(z0))), mark(x0)), MARK(U31(s(z0))))
   A__U21(tt, x0, U31(0)) -> c2(A__PLUS(a__U31(0), mark(x0)), MARK(U31(0)))
   A__U21(tt, x0, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, tt, U31(x1)) -> c2(MARK(U31(x1)))
   A__U21(tt, s(z0), U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U21(tt, 0, U41(x1, x2, x3)) -> c2(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(x1, z1, z2)) -> c2(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U21(tt, x0, U41(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U21(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(U31(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U41(U31(z0), x2, x3)))
   A__U21(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U41(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U41(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U41(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U21(tt, x0, U41(tt, x2, x3)) -> c2(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U21(tt, x0, U41(s(z0), x2, x3)) -> c2(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U21(tt, tt, U41(x1, x2, x3)) -> c2(MARK(U41(x1, x2, x3)))
   A__U21(tt, x0, U41(0, x2, x3)) -> c2(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U21(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U21(tt, x0, x(x1, U11(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x(x1, U11(z0, z1))))
   A__U21(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U21(tt, x0, x(x1, U31(z0))) -> c2(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(x(x1, U31(z0))))
   A__U21(tt, x0, x(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U21(tt, x0, x(x1, and(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x(x1, and(z0, z1))))
   A__U21(tt, x0, x(x1, isNat(z0))) -> c2(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x0)), MARK(x(x1, isNat(z0))))
   A__U21(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U21(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U21(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U21(tt, x0, x(U11(z0, z1), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(U11(z0, z1), x2)))
   A__U21(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U21(tt, x0, x(U31(z0), x2)) -> c2(A__PLUS(a__x(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(x(U31(z0), x2)))
   A__U21(tt, x0, x(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U21(tt, x0, x(and(z0, z1), x2)) -> c2(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x(and(z0, z1), x2)))
   A__U21(tt, x0, x(isNat(z0), x2)) -> c2(A__PLUS(a__x(a__isNat(z0), mark(x2)), mark(x0)), MARK(x(isNat(z0), x2)))
   A__U21(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U21(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U21(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U21(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2)))
   A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2)))
   A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1)))
   A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2)))
   A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2)))
   A__U21(tt, x0, and(U31(z0), x2)) -> c2(A__PLUS(a__and(a__U31(mark(z0)), x2), mark(x0)), MARK(and(U31(z0), x2)))
   A__U21(tt, x0, and(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2)))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(U21(U31(z0), x1, x2)))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U21(U41(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2)))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2)))
   A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

(237) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by 
   A__U21(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(plus(x0, U31(z0))))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1))))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U21(tt, plus(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(plus(U31(z0), x1)))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1)))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))

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

(238)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
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   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2)))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(U21(U31(z0), x1, x2)))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U21(U41(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2)))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2)))
   A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U21(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(plus(x0, U31(z0))))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1))))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U21(tt, plus(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(plus(U31(z0), x1)))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1)))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
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   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U21(U41(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2)))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2)))
   A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U21(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(plus(x0, U31(z0))))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1))))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U21(tt, plus(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(plus(U31(z0), x1)))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1)))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1


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

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

(240)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> mark(z0)
   a__U11(z0, z1) -> U11(z0, z1)
   a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U31(tt) -> 0
   a__U31(z0) -> U31(z0)
   a__U41(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(x(z0, z1)) -> a__and(a__isNat(z0), isNat(z1))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U11(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> a__U31(a__isNat(z0))
   a__x(z0, s(z1)) -> a__U41(a__and(a__isNat(z1), isNat(z0)), z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U31(z0)) -> a__U31(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U41(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c9(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1))
   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U41(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c9(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(plus(x(z0, z1), x1)) -> c14(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(plus(0, x1)) -> c14(A__AND(tt, isNat(x1)))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNAT(x(plus(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1)))
   A__ISNAT(x(s(z0), x1)) -> c16(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0)))
   A__ISNAT(x(x(z0, z1), x1)) -> c16(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(x(z0, z1)))
   A__ISNAT(x(0, x1)) -> c16(A__AND(tt, isNat(x1)))
   A__ISNAT(x(z0, x1)) -> c16(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c18(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(x(z0, z1), 0) -> c18(A__U11(a__and(a__isNat(z0), isNat(z1)), x(z0, z1)), A__ISNAT(x(z0, z1)))
   A__PLUS(0, 0) -> c18(A__U11(tt, 0))
   A__PLUS(z0, 0) -> c18(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c19(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__PLUS(x0, s(x(z0, z1))) -> c19(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__PLUS(x0, s(z0)) -> c19(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   A__X(x0, s(plus(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1)))
   A__X(x0, s(s(z0))) -> c22(A__U41(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0)))
   A__X(x0, s(x(z0, z1))) -> c22(A__U41(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), x(z0, z1), x0), A__AND(a__isNat(x(z0, z1)), isNat(x0)), A__ISNAT(x(z0, z1)))
   A__X(x0, s(z0)) -> c22(A__U41(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0))
   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__X(x0, s(0)) -> c22(A__U41(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
   MARK(U11(U11(z0, z1), x1)) -> c24(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1)) -> c24(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c24(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(U31(z0), x1)) -> c24(A__U11(a__U31(mark(z0)), x1), MARK(U31(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c24(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1)) -> c24(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c24(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNat(z0), x1)) -> c24(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(tt, x1)) -> c24(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c24(MARK(s(z0)))
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   A__U21(tt, U31(0), x1) -> c2(A__PLUS(mark(x1), a__U31(0)), MARK(x1))
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   A__U21(tt, U31(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(plus(z0, z1)))
   A__U21(tt, U31(x0), U31(z0)) -> c2(A__PLUS(a__U31(mark(z0)), a__U31(mark(x0))), MARK(U31(z0)))
   A__U21(tt, U31(x0), U41(z0, z1, z2)) -> c2(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U21(tt, U31(x0), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0))), MARK(x(z0, z1)))
   A__U21(tt, U31(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U31(mark(x0))), MARK(and(z0, z1)))
   A__U21(tt, U31(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U31(mark(x0))), MARK(isNat(z0)))
   A__U21(tt, U31(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U31(mark(x0))), MARK(s(z0)))
   A__U21(tt, U31(x0), x1) -> c2(MARK(x1))
   A__U21(tt, U31(x0), tt) -> c2(A__PLUS(tt, a__U31(mark(x0))))
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   A__U21(tt, U41(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(x(z0, z1)))
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   A__U21(tt, U41(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U21(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
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   A__U21(tt, isNat(0), x1) -> c2(MARK(x1))
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   A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
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   A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(U31(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__U31(mark(z0)), x2, x3), mark(x0)), MARK(U21(U31(z0), x2, x3)))
   A__U21(tt, x0, U21(U41(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U41(z0, z1, z2), x2, x3)))
   A__U21(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3)))
   A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3)))
   A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U21(tt, x0, plus(x1, U31(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__U31(mark(z0))), mark(x0)), MARK(plus(x1, U31(z0))))
   A__U21(tt, x0, plus(x1, U41(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U21(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1))))
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   A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U21(tt, x0, plus(U31(z0), x2)) -> c2(A__PLUS(a__plus(a__U31(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U31(z0), x2)))
   A__U21(tt, x0, plus(U41(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U21(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
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   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(plus(x0, U31(z0))))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1))))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U21(tt, plus(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(plus(U31(z0), x1)))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1)))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
S tuples:
   A__U11(tt, z0) -> c(MARK(z0))
   A__AND(tt, z0) -> c11(MARK(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(isNat(z0)) -> c33(A__ISNAT(z0))
   MARK(s(z0)) -> c35(MARK(z0))
   A__X(z0, 0) -> c21(A__ISNAT(z0))
   MARK(U31(z0)) -> c28(MARK(z0))
   A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U21(tt, tt, x1) -> c2(MARK(x1))
   A__U21(tt, U31(z0), x1) -> c3(A__PLUS(mark(x1), a__U31(mark(z0))), MARK(U31(z0)))
   A__U21(tt, U41(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U21(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U21(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0))
   A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U41(tt, U11(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1))
   A__U41(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U41(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U41(tt, U31(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(x1))
   A__U41(tt, U41(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(x1))
   A__U41(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U41(tt, and(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(x1))
   A__U41(tt, isNat(z0), x1) -> c7(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1))
   A__U41(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U41(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U41(tt, x0, U11(z0, z1)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1)))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U41(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U41(tt, x0, U31(z0)) -> c7(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(U31(z0)))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U41(mark(z0), z1, z2), mark(x0)), mark(U41(z0, z1, z2))), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U41(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U41(tt, x0, and(z0, z1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x0)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x0)), MARK(and(z0, z1)))
   A__U41(tt, x0, isNat(z0)) -> c7(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0)))
   A__U41(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U41(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U41(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U31(z0)) -> c8(A__PLUS(a__x(mark(U31(z0)), mark(x0)), a__U31(mark(z0))), A__X(mark(U31(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U41(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U41(z0, z1, z2)), mark(x0)), a__U41(mark(z0), z1, z2)), A__X(mark(U41(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U41(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, and(z0, z1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x0)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, isNat(z0)) -> c8(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U41(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U41(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U41(tt, U11(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1)))
   A__U41(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U41(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U41(tt, U31(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__U31(mark(z0))), mark(x1)), A__X(mark(x1), mark(U31(z0))), MARK(U31(z0)))
   A__U41(tt, U41(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2)))
   A__U41(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U41(tt, and(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__and(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(and(z0, z1))), MARK(and(z0, z1)))
   A__U41(tt, isNat(z0), x1) -> c8(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0)))
   A__U41(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U41(tt, x0, U11(z0, z1)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0))
   A__U41(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U41(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U41(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
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   A__U41(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U41(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U41(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
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   A__U41(tt, x0, U31(z0)) -> c9(A__PLUS(a__x(a__U31(mark(z0)), mark(x0)), mark(U31(z0))), MARK(U31(z0)))
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   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U41(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U41(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__PLUS(x0, s(x1)) -> c19(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
   A__PLUS(x0, s(0)) -> c19(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)))
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   A__X(x0, s(x1)) -> c22(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1))
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   A__U21(tt, x0, and(x(z0, z1), x2)) -> c2(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(x(z0, z1), x2)))
   A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2)))
   A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2)))
   A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2)))
   A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2)))
   A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2)))
   A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)))
   A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0))))
   A__U21(tt, x0, isNat(x(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(x(z0, z1))))
   A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1)))
   A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U21(tt, x0, s(U31(z0))) -> c2(A__PLUS(s(a__U31(mark(z0))), mark(x0)), MARK(s(U31(z0))))
   A__U21(tt, x0, s(U41(z0, z1, z2))) -> c2(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U21(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1))))
   A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1)))
   A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U21(tt, U11(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U31(mark(z0)), x1)), MARK(U11(U31(z0), x1)))
   A__U21(tt, U11(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U21(tt, U11(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(U11(x(z0, z1), x1)))
   A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1)))
   A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2)))
   A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U21(tt, U21(U31(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U31(mark(z0)), x1, x2)), MARK(U21(U31(z0), x1, x2)))
   A__U21(tt, U21(U41(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U21(U41(z0, z1, z2), x1, x2)))
   A__U21(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2)))
   A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2)))
   A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U21(tt, plus(x0, U31(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0)))), MARK(plus(x0, U31(z0))))
   A__U21(tt, plus(x0, U41(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U21(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1))))
   A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U21(tt, plus(U31(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U31(mark(z0)), mark(x1))), MARK(plus(U31(z0), x1)))
   A__U21(tt, plus(U41(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U21(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1)))
   A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U31(z0)) -> c3(A__PLUS(a__U31(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), U41(z0, z1, z2)) -> c3(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U21_3, a__U31_1, a__U41_3, a__and_2, a__isNat_1, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__X_2, A__U21_3, A__U41_3, A__PLUS_2

Compound Symbols:   c_1, c11_1, c15_1, c33_1, c35_1, c21_1, c28_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c14_2, c14_1, c16_2, c16_1, c18_2, c18_1, c19_3, c19_2, c22_3, c22_2, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c29_2, c29_1, c30_2, c30_1, c31_2, c31_1, c32_2, c32_1